Chapter 10 PHD Have Greater Earning Potential Than Those

Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine the null and alternative hypotheses for the proposed hypothesis test.

1)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for adults who are smokers is less than the mean forced vital capacity for adults who are former

smokers. He will use a paired sample to determine whether forced vital capacity increases, on

average, when adults stop smoking.

1)

A)

Let µ1 denote the mean forced vital capacity for adults who are smokers and let µ2 denote

the mean forced vital capacity for adults who are former smokers. The null and alternative

hypotheses are H0: µ1>µ2 and Ha: µ1<µ2.

B)

Let µ1 denote the mean forced vital capacity for adults who are smokers and let µ2 denote

the mean forced vital capacity for adults who are former smokers. The null and alternative

hypotheses are H0: µ1=µ2 and Ha: µ1>µ2.

C)

Let µ1 denote the mean forced vital capacity for adults who are smokers and let µ2 denote

the mean forced vital capacity for adults who are former smokers. The null and alternative

hypotheses are H0: µ1=µ2 and Ha: µ1<µ2.

D)

Let µ1 denote the mean forced vital capacity for adults who are smokers and let µ2 denote

the mean forced vital capacity for adults who are former smokers. The null and alternative

hypotheses are H0: µ1<µ2 and Ha: µ1>µ2.

2)

A nutritionist wants to investigate whether her new diet will be effective in helping women aged

30–40 to lose weight. She will use a paired sample to determine whether the mean weight of

women before going on this diet is greater than the mean weight of women after being on this diet

for two months.

2)

A)

Let µ1 denote the mean weight of women before going on this diet and let µ2 denote the

mean weight of women who have been on this diet for two months. The null and alternative

hypotheses are H0: µ1>µ2 and Ha: µ1<µ2.

B)

Let µ1 denote the mean weight of women before going on this diet and let µ2 denote the

mean weight of women who have been on this diet for two months. The null and alternative

hypotheses are H0: µ1>µ2 and Ha: µ1µ2.

C)

Let µ1 denote the mean weight of women before going on this diet and let µ2 denote the

mean weight of women who have been on this diet for two months. The null and alternative

hypotheses are H0: µ1=µ2 and Ha: µ1<µ2.

D)

Let µ1 denote the mean weight of women before going on this diet and let µ2 denote the

mean weight of women who have been on this diet for two months. The null and alternative

hypotheses are H0: µ1=µ2 and Ha: µ1>µ2.

3)

A pharmaceutical company wants to determine whether its new antianxiety medication has any

effect on resting pulse rate. They will use a paired sample to determine whether the mean resting

pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate

for adults who are taking the antianxiety medication.

3)

A)

Let µ1 denote the mean resting pulse rate for adults not taking the antianxiety medication and

let µ2 denote the mean resting pulse rate for adults who are taking the antianxiety

medication. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1>µ2.

B)

Let x1 denote the mean resting pulse rate for adults not taking the antianxiety medication and

let x2 denote the mean resting pulse rate for adults who are taking the antianxiety

medication. The null and alternative hypotheses are H0: x1=x2 and Ha: x1x2.

C)

Let µ1 denote the mean resting pulse rate for adults not taking the antianxiety medication and

let µ2 denote the mean resting pulse rate for adults who are taking the antianxiety

medication. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1µ2.

D)

Let µ1 denote the mean resting pulse rate for adults not taking the antianxiety medication and

let µ2 denote the mean resting pulse rate for adults who are taking the antianxiety

medication. The null and alternative hypotheses are H0: µ1µ2 and Ha: µ1=µ2.

4)

A company which designs sports shoes has made an improvement to their popular running shoe.

They hope that athletes wearing the new running shoe will be able to run faster over short

distances. They will use a paired sample to determine whether the mean time to run 100 meters for

sprinters wearing the new running shoe is less than the mean time to run the 100 meters for

sprinters wearing the old running shoe.

4)

A)

Let µ1 denote the mean time to run 100 meters for sprinters wearing the new running shoe

and let µ2 denote the mean time to run 100 meters for sprinters wearing the old running

shoe. The null and alternative hypotheses are H0: µ1<µ2 and Ha: µ1>µ2.

B)

Let µ1 denote the mean time to run 100 meters for sprinters wearing the new running shoe

and let µ2 denote the mean time to run 100 meters for sprinters wearing the old running

shoe. The null and alternative hypotheses are H0: µ1>µ2 and Ha: µ1<µ2.

C)

Let µ1 denote the mean time to run 100 meters for sprinters wearing the new running shoe

and let µ2 denote the mean time to run 100 meters for sprinters wearing the old running

shoe. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1µ2.

D)

Let µ1 denote the mean time to run 100 meters for sprinters wearing the new running shoe

and let µ2 denote the mean time to run 100 meters for sprinters wearing the old running

shoe. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1<µ2.

Provide an appropriate response.

5)

Suppose that x is a normally distributed variable on each of two populations. Independent samples

of sizes n1 and n2, respectively, are selected from the two populations. The mean of all possible

differences between the two sample means is equal to which of the following?

5)

A)

The sum of the two sample means

B)

The difference between the two sample means

C)

The sum of the two population means

D)

The difference between the two population means

6)

Which of the following statements regarding the equal–standard–deviations assumption of the

pooled t–test is the most accurate?

6)

A)

The pooled t–test is robust to moderate violations of the assumption regardless of the sample

sizes.

B)

The pooled t–test is extremely nonrobust to violations of the assumption.

C)

The pooled t–test is robust to moderate violations of the assumption provided the sample

sizes are large.

D)

The pooled t–test is robust to moderate violations of the assumption provided the sample

sizes are roughly equal.

Determine the null and alternative hypotheses for the proposed hypothesis test.

7)

A researcher wants to use a paired sample to determine whether the mean number of hours spent

exercising per week for married men differs from the mean number of hours spent exercising per

week for married women.

7)

A)

Let µ1 denote the mean number of hours spent exercising per week for married men and let

µ2 denote the mean number of hours spent exercising per week for married women. The null

and alternative hypotheses are H0: µ1µ2 and Ha: µ1=µ2.

B)

Let µ1 denote the mean number of hours spent exercising per week for married men and let

µ2 denote the mean number of hours spent exercising per week for married women. The null

and alternative hypotheses are H0: µ1=µ2 and Ha: µ1>µ2.

C)

Let x1 denote the mean number of hours spent exercising per week for married men and let

x2 denote the mean number of hours spent exercising per week for married women. The null

and alternative hypotheses are H0: x1=x2 and Ha: x1x2.

D)

Let µ1 denote the mean number of hours spent exercising per week for married men and let

µ2 denote the mean number of hours spent exercising per week for married women. The null

and alternative hypotheses are H0: µ1=µ2 and Ha: µ1µ2.

Provide an appropriate response.

8)

A researcher would like to conduct a hypothesis test to compare the mean SAT scores of students

who have received extra coaching and the mean test score of students who have not received extra

coaching. He will randomly select 15 students and will use the difference between the student’s

score after coaching and the student’s score before coaching as the paired–difference variable. He

obtains some normal probability plots of the sample data to determine whether it would be

reasonable to use a paired t–test. In which of the following situations would it be reasonable to use

a paired t–test ?

A: The distribution of the before test scores appears normal, the distribution of the after test scores

appears normal, however the distribution of the paired differences does not appear normal.

B: The distribution of the before test scores is nonnormal, the distribution of the after test scores is

nonnormal, however the distribution of the paired differences appears normal.

8)

A)

A only

B)

B only

C)

A and B

D)

Neither A nor B

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

9)

Suppose a researcher wants to perform a hypothesis test to compare the mean systolic

blood pressure for men with the mean systolic blood pressure for women, based on

independent samples. She obtains a random sample of 30 married couples and determines

the mean systolic blood pressure for the men, x1, and the mean systolic blood pressure for

the women, x2. She formulates the hypotheses as follows

H0: µ1=µ2

Ha: µ1µ2

and will reject the null hypothesis if x1–x2, the observed difference between the sample

means is too large. She will use a two–means z–test. Identify the flaw in her methodology.

9)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

10)

A test of abstract reasoning is given to a random sample of students before and after

completing a formal logic course. The results are shown below.

Before 74 83 75 88 84 63 93 84 91 77

After 73 77 70 77 74 67 95 83 84 75

At the 5% significance level, do the data provide sufficient evidence to conclude that that

the mean score after the course differs from the mean score before the course? Use the

critical–value approach.

10)

6

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t–procedures

satisfied. Perform the required hypothesis test by using either the critical–value approach or the P–value approach as

indicated.

11)

A researcher was interested in comparing the salaries of female and male employees at a

particular company. Independent simple random samples of 8 female employees and 15

male employees yielded the following weekly salaries (in dollars).

Female Male

495 722 518

760 562 904

556 880 1150

904 520 805

520 500 480

1005 1250 970

743 750 605

660 1640

At the 5% significance level, do the data provide sufficient evidence to conclude that at this

particular company the mean salary of female employees is less than the mean salary of

male employees? Use the critical–value approach. (Note: x1= 705.375, x2= 817.067, s1=

183.855, s2= 330.146.)

11)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

12)

A researcher was interested in comparing the GPAs of students at two different colleges.

Independent simple random samples of 8 students from college A and 13 students from

college B yielded the following GPAs.

College A College B

3.7 3.8 2.8

3.2 3.2 4.0

3.0 3.0 3.6

2.5 3.9 2.6

2.7 3.8 4.0

3.6 2.5 3.6

2.8 3.9

3.4

At the 10% significance level, do the data provide sufficient evidence to conclude that the

mean GPA of students at college A differs from the mean GPA of students at college B? Use

the critical–value approach.

(Note: x1= 3.1125, x2= 3.4385, s1= 0.4357, s2= 0.5485.)

12)

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t–procedures

satisfied. Perform the required hypothesis test by using either the critical–value approach or the P–value approach as

indicated.

13)

A researcher was interested in comparing the GPAs of students at two different colleges.

Independent simple random samples of 8 students from college A and 13 students from

college B yielded the following GPAs.

College A College B

3.7 3.8 2.8

3.2 3.2 4.0

3.0 3.0 3.6

2.5 3.9 2.6

2.7 3.8 4.0

3.6 2.5 3.6

2.8 3.9

3.4

At the 10% significance level, do the data provide sufficient evidence to conclude that the

mean GPA of students at college A differs from the mean GPA of students at college B? Use

the critical–value approach.

(Note: x1= 3.1125, x2= 3.4385, s1= 0.4357, s2= 0.5485.)

13)

Provide an appropriate response.

14)

Independent simple random samples of sizes 120 and 150 are taken from two populations

with the intent of performing a hypothesis test to compare the means. Prior data analyses

have indicated that the two population standard deviations are equal; however, the

variable under consideration is not normally distributed on either population. Is it

reasonable to use the pooled t–test in this situation? Explain your answer.

14)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

15)

A researcher was interested in comparing the salaries of female and male employees at a

particular company. Independent simple random samples of 8 female employees and 15

male employees yielded the following weekly salaries (in dollars).

Female Male

495 722 518

760 562 904

556 880 1150

904 520 805

520 500 480

1005 1250 970

743 750 605

660 1640

At the 5% significance level, do the data provide sufficient evidence to conclude that at this

company the mean salary of female employees is less than the mean salary of male

employees? Use the critical–value approach.

(Note: x1= 705.375, x2= 817.067, s1= 183.855, s2= 330.146.)

15)

Provide an appropriate response.

16)

Suppose that x is a normally distributed variable on each of two populations. Independent

samples of sizes n1 and n2, respectively, are selected from the two populations. Explain

the difference between x1–x2 and µ1–µ2.

16)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

17)

A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and

their competition scores were recorded before and after the training. The results are shown

below.

Subject A B C D E F G

Before 9.4 9.4 9.6 9.6 9.5 9.6 9.5

After 9.5 9.6 9.6 9.5 9.6 9.9 9.3

At the 1% significance level, do the data provide sufficient evidence to conclude that the

training technique is effective in raising scores? Use the critical–value approach.

17)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

18)

A paint manufacturer wished to compare the drying times of two different types of paint.

Independent simple random samples of 11 cans of type A and 9 cans of type B were

selected and applied to similar surfaces. The drying times, in hours, were recorded. The

summary statistics are as follows.

Type A Type B

x1=75.4 x2=64.0

s1= 4.5 s2= 5.1

n1=11 n2= 9

At the 1% significance level, do the data provide sufficient evidence to conclude that the

mean drying time for type A differs from the mean drying time for type B? Use the

critical–value approach.

18)

Provide an appropriate response.

19)

Manufacturer X has designed athletic footwear which it hopes will improve the

performance of athletes running the 100–meter sprint. It wishes to perform a hypothesis

test to compare the mean times of athletes in the 100–meter sprint running with

Manufacturer X’s footwear and with other shoes. Do you think that a paired t–test or a

pooled t–test would be more appropriate in this situation? Why? If you think that a paired

test is preferable, explain what would constitute a pair.

19)

20)

Suppose that you want to perform a hypothesis test based on independent simple random

samples to compare the means of two populations. Further suppose that the variable under

consideration is normally distributed on each of the two populations and that the

population standard deviations are unknown. If the sample standard deviations are 3.8

and 6.1, respectively, and the sample sizes are 25 and 60, respectively, would you use the

pooled or the nonpooled t–test? Explain your answer.

20)

21)

A teacher is interested in performing a hypothesis test to compare the mean math score of

the girls and the mean math score of the boys. She randomly selects 10 girls from the class

and then randomly selects 10 boys. She arranges the girls’ names alphabetically and uses

this list to assign each girl a number between 1 and 10. She does the same thing for the

boys. She pairs each girl with the boy having the same number. She then performs a paired

t–test. Do you think that in this situation a paired t–test is appropriate? Explain your

answer.

21)

22)

A researcher wants to compare the mean systolic blood pressures for adults ages 20–29 and

adults ages 30–39. Identify the variable under consideration and the two populations.

Suppose the researcher wants to perform a hypothesis test to decide whether the mean

systolic blood pressure for adults aged 20–29 is lower than the mean systolic blood

pressure for adults aged 30–39. State the null and alternative hypotheses for the hypothesis

test.

22)

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t–procedures

satisfied. Perform the required hypothesis test by using either the critical–value approach or the P–value approach as

indicated.

23)

A researcher was interested in comparing the resting pulse rate of people who exercise

regularly and people who do not exercise regularly. Independent simple random samples

of 16 people ages 30–40 who do not exercise regularly and 12 people ages 30–40 who do

exercise regularly were selected and the resting pulse rate of each person was measured.

The summary statistics are as follows.

Do Not Exercise Do Exercise

x1=73.4 x2=69.6

s1=10.9 s2=8.3

n1= 16 n2= 12

At the 2.5% significance level, do the data provide sufficient evidence to conclude that the

mean resting pulse rate of people who do not exercise regularly is greater than the mean

resting pulse rate of people who exercise regularly? Use the critical–value approach.

23)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

24)

A researcher was interested in comparing the amount of time spent watching television by

women and by men. Independent random samples of 14 women and 17 men were

selected and each person was asked how many hours he or she had watched television

during the previous week. The summary statistics are as follows:

Sample 1 (women) Sample 2 (men)

x1=11.7 x2=14.1

s1= 3.9 s2= 5.2

n1= 14 n2= 17

At the 5% significance level, do the data provide sufficient evidence to conclude that the

mean amount of time spent watching television by women is less than the mean amount

of time spent watching television by men? Use the P–value approach.

24)

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t–procedures

satisfied. Perform the required hypothesis test by using either the critical–value approach or the P–value approach as

indicated.

25)

A researcher was interested in comparing the heights of women in two different countries.

Independent simple random samples of 9 women from country A and 9 women from

country B yielded the following heights (in inches).

Country A Country B

64.1 65.3

66.4 60.2

61.7 61.7

62.0 65.8

67.3 61.0

64.9 64.6

64.7 60.0

68.0 65.4

63.6 59.0

At the 10% significance level, do the data provide sufficient evidence to conclude that the

mean height of women in country A is greater than the mean height of women in country

B? Use the critical–value approach.

(Note: x1= 64.744, x2= 62.556, s1= 2.192, s2= 2.697.)

25)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

26)

Five students took a math test before and after tutoring. Their scores were as follows.

Subject A B C D E

Before 77 73 67 73 77

After 81 82 65 76 89

At the 1% significance level, do the data provide sufficient evidence to conclude that the

mean score before tutoring differs from the mean score after tutoring? Use the P–value

approach.

26)

27)

Ten different families are tested for the number of gallons of water a day they use before

and after viewing a conservation video. The results are shown below.

Before 33 33 38 33 35 35 40 40 40 31

After 34 28 25 28 35 33 31 28 35 33

At the 5% significance level, do the data provide sufficient evidence to conclude that the

mean amount of water use after the viewing differs from the mean amount of water use

before the viewing? Use the critical–value approach.

27)

28)

The table below shows the weights, in pounds, of seven subjects before and after following

a particular diet for two months.

Subject A B C D E F G

Before 152 157 195 159 160 176 187

After 145 148 193 164 146 178 175

At the 1% significance level, do the data provide sufficient evidence to conclude that the

diet is effective in reducing weight? Use the P–value approach.

28)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

29)

A researcher was interested in comparing the resting pulse rates of people who exercise

regularly and people who do not exercise regularly. Independent simple random samples

of 16 people ages 30–40 who do not exercise regularly and 12 people ages 30–40 who

exercise regularly were selected, and the resting pulse rate (in beats per minute) of each

person was measured. The summary statistics are as follows.

Do Not Exercise Do Exercise

x1=73.7 x2=69.6

s1= 10.9 s2= 8.2

n1= 16 n2= 12

At the 2.5% significance level, do the data provide sufficient evidence to conclude that the

mean resting pulse rate of people who do not exercise regularly is greater than the mean

resting pulse rate of people who exercise regularly? Use the critical–value approach.

29)

Provide an appropriate response.

30)

A researcher wishes to compare the incomes of men and women. She selects a random

sample of 80 married women. She records the weekly income of each of these women.

Using the husbands of these women as the sample of men, she also records the weekly

income of each man. She obtains the following summary statistics.

Women Men

x1= 520 x2= 590

s1= 220 s2= 240

n1= 80 n2= 80

Incomes are known to be normally distributed for both populations (women and men).

Furthermore, the two population standard deviations are known to be equal. Is it

reasonable to use the pooled t–test on these data? Explain your answer.

30)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

31)

The table below shows the weights, in pounds, of seven subjects before and after following

a particular diet for two months.

Subject A B C D E F G

Before 186 153 170 151 194 166 156

After 179 144 168 156 180 168 144

At the 1% significance level, do the data provide sufficient evidence to conclude that the

diet is effective in reducing weight? Use the critical–value approach.

31)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

32)

A researcher was interested in comparing the GPAs of students at two different colleges.

Independent random samples of 8 students from college A and 13 students from college B

yielded the following GPAs:

College A College B

3.7 3.8 2.8

3.2 3.2 4.0

3.0 3.0 3.6

2.5 3.9 2.6

2.7 3.8 4.0

3.6 2.5 3.6

2.8 3.9

3.4

At the 10% significance level, do the data provide sufficient evidence to conclude that the

mean GPA of students at college A differs from the mean GPA of students at college B? Use

the P–value approach.

(Note: x1= 3.1125, x2= 3.4385, s1= 0.4357, s2= 0.5485.)

32)

Provide an appropriate response.

33)

The pooled t–test requires the assumption that the two population standard deviations be

equal. What methods are available for checking this assumption? Which of these methods

is not recommended and why is it not recommended?

33)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

34)

A paint manufacturer wishes to compare the drying times of two different types of paint.

Independent random samples of 11 cans of type A and 9 cans of type B were selected and

applied to similar surfaces. The drying times (in minutes) were recorded. The summary

statistics are as follows.

Type A Type B

x1=75.0 x2=63.3

s1= 4.5 s2= 5.1

n1= 11 n2= 9

Do the data provide sufficient evidence to conclude that the mean drying time for type A

differs from the mean drying time for type B? Perform a t–test at the 1% significance level.

Use the P–value approach.

34)

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t–procedures

satisfied. Perform the required hypothesis test by using either the critical–value approach or the P–value approach as

indicated.

35)

A researcher wishes to determine whether the systolic blood pressure of people who follow

a vegetarian diet is, on average, lower than the systolic blood pressure of those who follow

a nonvegetarian diet.

Independent simple random samples of 85 vegetarians and 75 nonvegetarians yielded the

following sample statistics:

Vegetarians Nonvegetarians

n1= 85 n2= 75

x1= 124.1 x2= 138.7

s1= 38.7 s2= 39.2

Use the sample data to test the claim that the mean systolic blood pressure for vegetarians

is lower than the mean systolic blood pressure for nonvegetarians. Test the claim using a

significance level of 0.01. Use the P–value approach.

35)

Provide an appropriate response.

36)

Suppose a researcher wants to perform a hypothesis test to decide whether the mean

systolic blood pressure for adults aged 20–29 is lower than the mean systolic blood

pressure for adults aged 30–39. State the null and alternative hypotheses for the hypothesis

test. Discuss the basic strategy for performing this hypothesis test, based on independent

samples.

36)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

37)

A coach uses a new technique in training middle distance runners. The times, in seconds,

for 8 different athletes to run 800 meters before and after this training are shown below.

Athlete A B C D E F G H

Before 112.9 113.4 120 116.5 116.6 116.3 114.7 111.1

After 113.5 112.1 117.6 117.3 114.8 116.4 111.1 107.2

At the 5% significance level, do the data provide sufficient evidence that the training helps

to improve times for the 800 meters? Use the P–value approach.

37)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

38)

A researcher wishes to determine whether the systolic blood pressure of people who follow

a vegetarian diet is, on average, lower than the systolic blood pressure of those who do not

follow a vegetarian diet.

Independent simple random samples of 85 vegetarians and 75 nonvegetarians yielded the

following sample statistics:

Vegetarians Nonvegetarians

n1= 85 n2= 75

x1= 124.1 x2= 138.7

s1= 38.7 s2= 39.2

Use a significance level of 0.01 to test the claim that the mean systolic blood pressure for

vegetarians is lower than the mean systolic blood pressure for nonvegetarians. Use the

P–value approach.

38)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

39)

A coach uses a new technique in training middle distance runners. The times, in seconds,

for 8 different athletes to run 800 meters before and after this training are shown below.

Athlete A B C D E F G H

Before 111 112.7 108.8 119 112.7 118 108.3 109.9

After 111.6 111.4 106.4 119.8 110.9 118.1 104.7 106

At the 5% significance level, do the data provide sufficient evidence that the training helps

to improve times for the 800 meters? Use the critical–value approach.

39)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

40)

A researcher was interested in comparing the response times of two different cab

companies. Companies A and B were each called at 50 randomly selected times. The calls

to company A were made independently of the calls to company B. The response times for

each call were recorded. The summary statistics were as follows:

Company A Company B

Mean response time 7.6 minutes 6.9 minutes

Standard deviation 1.4 minutes 1.7 minutes

At the 0.02 level of significance, do the data provide sufficient evidence to conclude that

the mean response time for company A differs from the mean response time for company

B? Use the P–value approach.

40)

Provide an appropriate response.

41)

In comparing the means of two populations, some methods are based on independent

samples and some are based on paired samples. Explain the difference between

independent and paired samples. Give an example of each type of sample.

41)

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t–procedures

satisfied. Perform the required hypothesis test by using either the critical–value approach or the P–value approach as

indicated.

42)

A researcher was interested in comparing the amount of time spent watching television by

women and by men. Independent simple random samples of 14 women and 17 men were

selected, and each person was asked how many hours he or she had watched television

during the previous week. The summary statistics are as follows.

Women Men

x1=11.2 x2=17.4

s1=4.3 s2=4.7

n1= 14 n2= 17

At the 5% significance level, do the data provide sufficient evidence to conclude that the

mean time spent watching television by women is less than the mean time spent watching

television by men? Use the critical–value approach.

42)

Preliminary data analyses indicate that you can reasonably use nonpooled t–procedures on the given data. Apply a

nonpooled t–test to perform the required hypothesis test, using either the critical–value approach or the P–value approach

as indicated.

43)

A researcher was interested in comparing the amount of time spent watching television by

women and by men. Independent simple random samples of 14 women and 17 men were

selected, and each person was asked how many hours he or she had watched television

during the previous week. The summary statistics are as follows.

Women Men

x1=11.8 x2=14.0

s1= 3.9 s2= 5.2

n1= 14 n2= 17

At the 5% significance level, do the data provide sufficient evidence to conclude that the

mean amount of time spent watching television by women is less than the mean amount

of time spent watching television by men? Use the critical–value approach.

43)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

44)

A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and

their competition scores were recorded before and after the training. The results are shown

below.

Subject A B C D E F G

Before 9.4 9.6 9.5 9.7 9.4 9.4 9.4

After 9.5 9.8 9.5 9.6 9.5 9.7 9.2

At the 1% significance level, do the data provide sufficient evidence to conclude that the

training technique is effective in raising scores? Use the P–value approach.

44)

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t–procedures

satisfied. Perform the required hypothesis test by using either the critical–value approach or the P–value approach as

indicated.

45)

A researcher was interested in comparing the heights of women in two different countries.

Independent simple random samples of 9 women from country A and 9 women from

country B yielded the following heights (in inches).

Country A Country B

64.1 65.3

66.4 60.2

61.7 61.7

62.0 65.8

67.3 61.0

64.9 64.6

64.7 60.0

68.0 65.4

63.6 59.0

At the 10% significance level, do the data provide sufficient evidence to conclude that the

mean height of women in country A is greater than the mean height of women in country

B? Use the P–value approach.

(Note: x1= 64.744, x2= 62.556, s1= 2.192, s2= 2.697.)

45)

46)

A researcher was interested in comparing the response times of two different cab

companies. Companies A and B were each called at 50 randomly selected times. The calls

to company A were made independently of the calls to company B. The response times for

each call were recorded. The summary statistics were as follows:

Company A Company B

Mean response time 7.6 minutes 6.9 minutes

Standard deviation 1.4 minutes 1.7 minutes

At the 0.02 level of significance, do the data provide sufficient evidence to conclude that

the mean response time for company A differs from the mean response time for company

B? Use the P–value approach.

46)

Preliminary data analyses indicates that use of a paired t–test is reasonable. Perform the hypothesis test by using either

the critical–value approach or the P–value approach as indicated. Assume that the null hypothesis is H0 : µ1=µ2.

47)

Five students took a math test before and after tutoring. Their scores were as follows.

Subject A B C D E

Before 75 71 73 66 70

After 79 80 71 69 82

At the 1% significance level, do the data provide sufficient evidence to conclude that the

mean score before tutoring differs from the mean score after tutoring? Use the

critical–value approach.

47)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

48)

Suppose that you want to perform a hypothesis test based on independent simple random samples

to compare the means of two populations. Further suppose that either the variable under

consideration is normally distributed on each of the two populations or the sample sizes are large.

True or false? If the population standard deviations are quite different, then using the pooled t–test

can result in a significantly smaller Type I error probability than the one specified.

48)

A)

True

B)

False

Summary statistics are given for independent simple random samples from two populations. Use the nonpooled t–test to

conduct the required hypothesis test.

49)

x1=73.1, s1= 10.9, n1= 16, x2=68.0, s2= 8.2, n2= 12

Perform a right–tailed hypothesis test using a significance level of  = 0.05.

49)

A)

Test statistic: t =1.413

Critical value = 1.708

Do not reject H0

B)

Test statistic: t =1.413

Critical value = 1.706

Do not reject H0

C)

Test statistic: t = 2.635

Critical value = 1.706

Reject H0

D)

Test statistic: t = 2.635

Critical value = 1.708

Reject H0

Summary statistics are given for independent simple random samples from two populations. Use the nonpooled

t–interval procedure to obtain the specified confidence interval.

50)

x1=12.0, s1= 3.9, n1= 14, x2=14.3, s2= 5.2, n2= 17

99% confidence interval

50)

A)

–6.82 to 2.22

B)

–6.44 to 1.84

C)

–6.34 to 1.74

D)

–6.94 to 2.34

Solve the problem.

51)

A company which designs sports shoes has made an improvement to their popular running shoe.

They hope that athletes wearing the new running shoe will be able to run faster over short

distances. They will use a paired sample to determine whether the mean time to run 100 meters for

sprinters wearing the new running shoe is less than the mean time to run the 100 meters for

sprinters wearing the old running shoe. Identify the two populations for the proposed hypothesis

test.

51)

A)

Running shoes of the new design and running shoes of the existing design

B)

Athletes and non athletes

C)

Sprinters wearing the new running shoe and sprinters wearing the old running shoe

D)

Athletes who run the 100 meters and athletes who run other distances

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

52)

A researcher wants to perform a hypothesis test to determine whether the mean credit card debt for

credit card holders aged 18–35 is greater than the mean credit card debt for credit card holders aged

over 35.

52)

A)

Two tailed

B)

Left tailed

C)

Right tailed

53)

A nutritionist wants to investigate whether her new diet will be effective in helping women aged

30–40 to lose weight. She will use a paired sample to determine whether the mean weight of

women before going on this diet is greater than the mean weight of women after being on this diet

for two months.

53)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Solve the problem.

54)

A researcher is interested in comparing the resting pulse rate of women who exercise regularly and

women who do not exercise regularly. She wants to perform a hypothesis test to determine

whether the mean resting pulse rate of women who exercise at least 6 hours per week is less than

the mean resting pulse rate of women who exercise less than 6 hours per week. Identify the

variable for the proposed hypothesis test.

54)

A)

Difference between mean resting pulse rate of women who exercise regularly and mean

resting pulse rate of women who do not exercise regularly

B)

Resting pulse rate

C)

Mean resting pulse rate

D)

Hours of exercise per week

Provide an appropriate response.

55)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for adults who are smokers is less than the mean forced vital capacity for adults who are former

smokers. He will use a paired sample to determine whether forced vital capacity increases, on

average, when adults stop smoking. Identify the pairs for the proposed hypothesis test.

55)

A)

Each pair consists of an adult who smokes and the same person after they stop smoking.

B)

Each pair consists of a randomly selected adult who smokes and a randomly selected adult

who has stopped smoking.

C)

Each pair consists of the mean FVC of smokers and the mean FVC of former smokers.

D)

Each pair consists of the FVC of a randomly selected adult who smokes and the FVC of a

randomly selected adult who has stopped smoking.

Determine the null and alternative hypotheses for the proposed hypothesis test.

56)

A researcher is interested in determining whether men who have completed a postgraduate degree

(master’s or Phd) have greater earning potential than those who have completed a Bachelor’s

degree only. She will perform a hypothesis test to determine whether the mean salary of men who

have completed a postgraduate degree is greater than the mean salary of men with a Bachelor’s

degree only.

56)

A)

Let x1 denote the mean salary of men with a postgraduate degree and let x2 denote the mean

salary of men with a Bachelor’s degree only. The null and alternative hypotheses are

H0: x1=x2 and Ha: x1>x2.

B)

Let µ1 denote the mean salary of men with a postgraduate degree and let µ2 denote the mean

salary of men with a Bachelor’s degree only. The null and alternative hypotheses are

H0: µ1>µ2 and Ha: µ1<µ2.

C)

Let µ1 denote the mean salary of men with a postgraduate degree and let µ2 denote the mean

salary of men with a Bachelor’s degree only. The null and alternative hypotheses are

H0: µ1=µ2 and Ha: µ1<µ2.

D)

Let µ1 denote the mean salary of men with a postgraduate degree and let µ2 denote the mean

salary of men with a Bachelor’s degree only. The null and alternative hypotheses are

H0: µ1=µ2 and Ha: µ1>µ2.

Solve the problem.

57)

A researcher is interested in determining whether men who have completed a postgraduate degree

(master’s or Phd) have greater earning potential than those who have completed a Bachelor’s

degree only. She will perform a hypothesis test to determine whether the mean salary of men who

have completed a postgraduate degree is greater than the mean salary of men with a Bachelor’s

degree only. Identify the variable for the proposed hypothesis test.

57)

A)

Difference between mean salary of men with a Bachelor’s degree only and mean salary of

men who have completed a postgraduate degree

B)

Salary

C)

Highest level of education completed

D)

Mean salary

Provide an appropriate response.

58)

A pharmaceutical company wants to determine whether its new antianxiety medication has any

effect on resting pulse rate. They will use a paired sample to determine whether the mean resting

pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate

for adults who are taking the antianxiety medication. Identify the pairs for the proposed hypothesis

test.

58)

A)

Each pair consists of an adult not on the antianxiety medication and the same person on the

antianxiety medication

B)

Each pair consists of a randomly selected adult who is not on the antianxiety medication and

a randomly selected adult who is on the antianxiety medication

C)

Each pair consists of the mean resting pulse rate of adults not on the antianxiety medication

and the mean resting pulse rate of adults on the antianxiety medication

D)

Each pair consists of an adult who is on the antianxiety medication and their resting pulse

rate

59)

Suppose that you want to perform a hypothesis test based on independent simple random samples

to compare the means of two populations. Further suppose that either the variable under

consideration is normally distributed on each of the two populations or the sample sizes are large.

True or false? If the population standard deviations are equal, then, on average, the pooled t–test is

slightly more powerful than the nonpooled t–test.

59)

A)

True

B)

False

Solve the problem.

60)

A researcher wants to perform a hypothesis test to determine whether the mean length of

marriages in California differs from the mean length of marriages in Texas. Identify the variable for

the proposed hypothesis test.

60)

A)

Percent of marriages ending in divorce

B)

Length of marriage

C)

State

D)

Difference between mean length of marriages in California and mean length of marriages in

Texas

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

61)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for adults who are smokers is less than the mean forced vital capacity for adults who are former

smokers. He will use a paired sample to determine whether forced vital capacity increases, on

average, when adults stop smoking.

61)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Provide an appropriate response.

62)

A researcher wants to use a paired sample to determine whether the mean number of hours spent

exercising per week for married men differs from the mean number of hours spent exercising per

week for married women. Identify the pairs for the proposed hypothesis test.

62)

A)

Hours of exercise per week for each woman together with hours of exercise per week of her

husband

B)

Married couples

C)

Married men and married women

D)

A married person together with the numbers of hours per week that they exercise

Solve the problem.

63)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for women is less than the mean forced vital capacity for men. Identify the variable for the

proposed hypothesis test.

63)

A)

Forced vital capacity

B)

Mean forced vital capacity

C)

Difference between mean forced vital capacity for women and mean forced vital capacity for

men

D)

Gender

Use the paired t–interval procedure to obtain the required confidence interval. You may assume that the conditions for

using the procedure are satisfied.

64)

If d= 3.125, sd= 2.911, and n = 8, determine a 99% confidence interval for µ1–µ2.

64)

A)

1.851 to 4.399

B)

–0.476 to 6.726

C)

0.215 to 6.035

D)

1.851 to 6.726

Summary statistics are given for independent simple random samples from two populations. Use the pooled t–interval

procedure to obtain the specified confidence interval.

65)

x1=71.4, s1=3.8, n1= 11, x2=68.3, s2=3.2, n2= 9

Determine a 99% confidence interval.

65)

A)

–1.49 to 7.69

B)

–2.22 to 8.42

C)

–0.97 to 7.17

D)

–0.09 to 6.29

Provide an appropriate response.

66)

Suppose that you want to perform a hypothesis test based on independent simple random samples

to compare the means of two populations. Further suppose that either the variable under

consideration is normally distributed on each of the two populations or the sample sizes are large.

True or false? If the population standard deviations are equal, then the pooled t–test gives a larger

probability of a Type II error than the nonpooled t–test.

66)

A)

True

B)

False

Summary statistics are given for independent simple random samples from two populations. Use the pooled t–interval

procedure to obtain the specified confidence interval.

67)

x1=72.4, s1=10.7, n1= 16, x2=68.7, s2=8.1, n2= 12

Determine a 90% confidence interval.

67)

A)

–0.37 to 7.77

B)

–3.27 to 10.67

C)

–2.61 to 10.01

D)

–1.16 to 8.56

Provide an appropriate response.

68)

True or false? In the context of the pooled t–test for two population means, the pooled sample

standard deviation, sp, always lies between the two sample standard deviations, s1 and s2.

68)

A)

True

B)

False

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

69)

A researcher wants to perform a hypothesis test to determine whether the mean length of

marriages in California differs from the mean length of marriages in Texas.

69)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Apply the nonpooled t–interval procedure to obtain the required confidence interval. You may assume that the

assumptions for using the procedure are satisfied.

70)

A researcher was interested in comparing the GPAs of students at two different colleges.

Independent simple random samples of 8 students from college A and 13 students from college B

yielded the following GPAs.

College A College B

3.7 3.8 2.8

3.2 3.2 4.0

3.0 3.0 3.6

2.5 3.9 2.6

2.7 3.8 4.0

3.6 2.5 3.6

2.8 3.9

3.4

Determine a 95% confidence interval for the difference, µ1–µ2, between the mean GPA of college

A students and the mean GPA of college B students.

(Note: x1= 3.1125, x2= 3.4385, s1= 0.4357, s2= 0.5485.)

70)

A)

–0.75 to 0.10

B)

–0.78 to 0.13

C)

–0.81 to 0.15

D)

–0.70 to 0.05

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

71)

A pharmaceutical company wants to determine whether its new antianxiety medication has any

effect on resting pulse rate. They will use a paired sample to determine whether the mean resting

pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate

for adults who are taking the antianxiety medication.

71)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Apply the nonpooled t–interval procedure to obtain the required confidence interval. You may assume that the

assumptions for using the procedure are satisfied.

72)

A researcher was interested in comparing the salaries of female and male employees at a particular

company. Independent simple random samples of 8 female employees and 15 male employees

yielded the following weekly salaries (in dollars).

Female Male

495 722 518

760 562 904

556 880 1150

904 520 805

520 500 480

1005 1250 970

743 750 605

660 1640

Determine a 98% confidence interval for the difference, µ1–µ2, between the mean weekly salaries

of female employees and the mean weekly salaries of male employees at this particular company.

(Note: x1= 705.375, x2= 817.067, s1= 183.855, s2= 330.146.)

72)

A)

–$346 to $123

B)

–$431 to $208

C)

–$383 to $159

D)

–$297 to $73

Solve the problem.

73)

A nutritionist wants to investigate whether her new diet will be effective in helping women aged

30–40 to lose weight. She will use a paired sample to determine whether the mean weight of

women before going on this diet is greater than the mean weight of women after being on this diet

for two months. Identify the two populations for the proposed hypothesis test.

73)

A)

Women aged 30–40 who have not been on this diet and women aged 30–40 who have been on

this diet for two months

B)

Adults aged 30–40 who have not been on this diet and adults aged 30–40 who have been on

this diet for two months

C)

Women aged 30–40 and women of other ages

D)

Women aged 30–40 who are overweight and women aged 30–40 who are not overweight

A confidence interval (CI) for the difference µ1–µ2 between two population means is given. Interpret the confidence

interval.

74)

98% CI from –30 to 230

74)

A)

We can be 98% confident that µ1–µ2 lies somewhere between –30 and 230. Equivalently, we

can be 98% confident that µ1 is somewhere between 30 less than and 230 more than µ2.

B)

We can be 98% confident that µ1 and µ2 both lie somewhere between –30 and 230.

C)

We can be 98% confident that µ2–µ1 lies somewhere between 30 and 230. Equivalently, we

can be

98% confident that µ2 is somewhere between 30 less than and 230 more than µ2.

D)

We can be 98% confident that µ1–µ2 lies somewhere between 30 and 230. Equivalently, we

can be

98% confident that µ1 is somewhere between 30 less than and 230 more than µ2.

Solve the problem.

75)

A researcher is interested in determining whether men who have completed a postgraduate degree

(master’s or Phd) have greater earning potential than those who have completed a Bachelor’s

degree only. She will perform a hypothesis test to determine whether the mean salary of men who

have completed a postgraduate degree is greater than the mean salary of men with a Bachelor’s

degree only. Identify the two populations for the proposed hypothesis test.

75)

A)

Men with a high salary and men with a low salary

B)

Men with a Bachelor’s degree only and men who have completed a postgraduate degree

C)

Salaries of men with a Bachelor’s degree only and salaries of men who have completed a

postgraduate degree

D)

Adults with a Bachelor’s degree only and adults who have completed a postgraduate degree

Apply the nonpooled t–interval procedure to obtain the required confidence interval. You may assume that the

assumptions for using the procedure are satisfied.

76)

A researcher was interested in comparing the heights of women in two different countries.

Independent simple random samples of 9 women from country A and 9 women from country B

yielded the following heights (in inches).

Country A Country B

64.1 65.3

66.4 60.2

61.7 61.7

62.0 65.8

67.3 61.0

64.9 64.6

64.7 60.0

68.0 65.4

63.6 59.0

Determine a 90% confidence interval for the difference, µ1–µ2, between the mean height of

women in country A and the mean height of women in country B.

(Note: x1= 64.744, x2= 62.556, s1= 2.192, s2= 2.697.)

76)

A)

0.63 to 3.74 inches

B)

–0.83 to 5.2 inches

C)

–1.22 to 5.60 inches

D)

0.16 to 4.22 inches

Solve the problem.

77)

A researcher wants to perform a hypothesis test to determine whether the mean credit card debt for

credit card holders aged 18–35 is greater than the mean credit card debt for credit card holders aged

over 35. Identify the two populations for the proposed hypothesis test.

77)

A)

Adults aged 18–30 and adults over 35

B)

Adults with credit card debt and adults without credit card debt

C)

Credit card debts for credit card holders aged 18–35 and credit card debts for credit card

holders over 35

D)

Credit card holders aged 18–30 and credit card holders aged over 35

Use the paired t–interval procedure to obtain the required confidence interval. You may assume that the conditions for

using the procedure are satisfied.

78)

A test of abstract reasoning is given to a random sample of students before and after completing a

formal logic course. The results are shown below.

Before After

74 72

81 86

85 83

67 76

92 95

71 66

61 67

78 81

64 71

80 88

Determine a 95% confidence interval for the difference between the mean score after completing the

course and the mean score before completing the course.

78)

A)

–0.2 to 6.6

B)

0.1 to 6.3

C)

–0.8 to 7.2

D)

–0.5 to 6.9

Apply the nonpooled t–interval procedure to obtain the required confidence interval. You may assume that the

assumptions for using the procedure are satisfied.

79)

A researcher was interested in comparing the amount of time spent watching television by women

and by men. Independent simple random samples of 14 women and 17 men were selected, and

each person was asked how many hours he or she had watched television during the previous

week. The summary statistics are as follows.

Women Men

x1=12.2 x2=14.2

s1= 3.9 s2= 5.2

n1= 14 n2= 17

Determine a 99% confidence interval for the difference, µ1–µ2, between the mean television

watching times for women and men.

79)

A)

–6.64 to 2.64 hours

B)

–6.52 to 2.52 hours

C)

–6.14 to 2.14 hours

D)

–6.04 to 2.04 hours

80)

A paint manufacturer wished to compare the drying times of two different types of paint.

Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and

applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are

as follows.

Type A Type B

x1=76.1 x2=63.0

s1= 4.5 s2= 5.1

n1= 11 n2= 9

Determine a 98% confidence interval for the difference, µ1–µ2, between the mean drying time for

type A and the mean drying time for type B.

80)

A)

7.78 to 18.42 hours

B)

7.62 to 18.58 hours

C)

7.55 to 18.65 hours

D)

7.48 to 18.72 hours

Provide an appropriate response.

81)

Suppose that you want to perform a hypothesis test based on independent simple random samples

to compare the means of two populations. Further suppose that either the variable under

consideration is normally distributed on each of the two populations or the sample sizes are large.

True or false? If you are reasonably sure that the populations have nearly equal standard

deviations, then you should use a pooled t–procedure.

81)

A)

True

B)

False

Summary statistics are given for independent simple random samples from two populations. Use the nonpooled

t–interval procedure to obtain the specified confidence interval.

82)

x1=77.9, s1= 4.5, n1= 11, x2=66.3, s2= 5.1, n2= 9

98% confidence interval

82)

A)

6.05 to 17.15

B)

5.98 to 17.22

C)

6.28 to 16.92

D)

6.12 to 17.08

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

83)

A company which designs sports shoes has made an improvement to their popular running shoe.

They hope that athletes wearing the new running shoe will be able to run faster over short

distances. They will use a paired sample to determine whether the mean time to run 100 meters for

sprinters wearing the new running shoe is less than the mean time to run the 100 meters for

sprinters wearing the old running shoe.

83)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Solve the problem.

84)

A variable of two populations has a mean of 18 and a standard deviation of 13 for one of the

populations and a mean of 26 and a standard deviation of 4 for the other population. For

independent samples of sizes 6 and 20 , respectively, find the standard deviation of x1–x2. Round

your answer to the nearest hundredth.

84)

A)

5.23

B)

1.54

C)

28.97

D)

5.38

85)

A nutritionist wants to investigate whether her new diet will be effective in helping women aged

30–40 to lose weight. She will use a paired sample to determine whether the mean weight of

women before going on this diet is greater than the mean weight of women after being on this diet

for two months. Identify the variable for the proposed hypothesis test.

85)

A)

Type of diet

B)

Age

C)

Gender

D)

Weight

Solve.

86)

A variable of two populations has a mean of 25 and a standard deviation of 7 for one of the

populations and a mean of 25 and a standard deviation of 11 for the other population. Determine

the percentage of all pairs of independent samples of sizes 3 and 9, respectively, from the two

populations with the property that the difference x1–x2 between the samples means is between

–5.46 and 5.46.

86)

A)

95.44%

B)

84.13%

C)

71.26%

D)

68.26%

Solve the problem.

87)

A researcher wants to perform a hypothesis test to determine whether the mean length of

marriages in California differs from the mean length of marriages in Texas. Identify the two

populations for the proposed hypothesis test.

87)

A)

Married men and married women

B)

Lengths of California marriages and lengths of Texas marriages

C)

Marriages in California and marriages in Texas

D)

Adults living in California and adults living in Texas

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

88)

A researcher is interested in determining whether men who have completed a postgraduate degree

(master’s or Phd) have greater earning potential than those who have completed a Bachelor’s

degree only. She will perform a hypothesis test to determine whether the mean salary of men who

have completed a postgraduate degree is greater than the mean salary of men with a Bachelor’s

degree only.

88)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Solve the problem.

89)

A pharmaceutical company wants to determine whether its new antianxiety medication has any

effect on resting pulse rate. They will use a paired sample to determine whether the mean resting

pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate

for adults who are taking the antianxiety medication. Identify the two populations for the proposed

hypothesis test.

89)

A)

Adults who suffer side effects from the antianxiety medication and adults who do not suffer

side effects from the antianxiety medication

B)

Adults with high resting pulse rate and adults with low resting pulse rate

C)

Adults suffering from anxiety and adults not suffering from anxiety

D)

Adults not taking the antianxiety medication and adults taking the antianxiety medication

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

90)

A researcher is interested in comparing the resting pulse rate of women who exercise regularly and

women who do not exercise regularly. She wants to perform a hypothesis test to determine

whether the mean resting pulse rate of women who exercise at least 6 hours per week is less than

the mean resting pulse rate of women who exercise less than 6 hours per week.

90)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Solve the problem.

91)

A researcher wants to perform a hypothesis test to determine whether the mean credit card debt for

credit card holders aged 18–35 is greater than the mean credit card debt for credit card holders aged

over 35. Identify the variable for the proposed hypothesis test.

91)

A)

Mean credit card debt

B)

Difference between mean credit card debt for credit card holders aged 18–35 and mean credit

card debt for credit card holders aged over 35

C)

Age

D)

Credit card debt

Apply the pooled t–interval procedure to obtain the required confidence interval. You may assume that the assumptions

for using the procedure are satisfied.

92)

A researcher was interested in comparing the resting pulse rates of people who exercise regularly

and people who do not exercise regularly. Independent simple random samples were obtained of

16 people aged 30–40 who do not exercise regularly and 12 people aged 30–40 who do exercise

regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary

statistics are as follows.

Do Not Exercise Do Exercise

x1=72.2 x2=68.4

s1=10.2 s2=8.5

n1= 16 n2= 12

Determine a 90% confidence interval for the difference between the mean pulse rate of people who

do not exercise regularly and the mean pulse rate of people who exercise regularly.

92)

A)

–0.98 to 8.58 beats per minute

B)

–3.05 to 10.65 beats per minute

C)

–2.40 to 10.00 beats per minute

D)

–0.20 to 7.80 beats per minute

Solve the problem.

93)

A company which designs sports shoes has made an improvement to their popular running shoe.

They hope that athletes wearing the new running shoe will be able to run faster over short

distances. They will use a paired sample to determine whether the mean time to run 100 meters for

sprinters wearing the new running shoe is less than the mean time to run the 100 meters for

sprinters wearing the old running shoe. Identify the variable for the proposed hypothesis test.

93)

A)

Type of athlete

B)

Distance run

C)

Type of sports shoe worn

D)

Time to run 100 meters

Provide an appropriate response.

94)

Suppose that you want to perform a nonpooled t–test based on independent simple random

samples to compare the means of two populations . Further suppose that the variable under

consideration is normally distributed on each of the two populations. Given the summary statistics

below, what degrees of freedom would you use to obtain the critical value?

Sample 1 Sample 2

s12= 16.8 s22= 19.3

n1= 14 n2= 12

94)

A)

23

B)

24

C)

25

D)

22

D

Use the paired t–interval procedure to obtain the required confidence interval. You may assume that the conditions for

using the procedure are satisfied.

95)

The table below shows the weight, in pounds, of 9 subjects before and after following a particular

diet for two months.

Subject Before After

A 168 164

B 180 172

C 157 162

D 132 121

E 202 183

F 124 126

G 190 180

H 210 195

I 171 163

Determine a 99% confidence interval for the weight loss that would be obtained, on average, by

following the diet for two months.

95)

A)

–0.2 to 15.3 lb

B)

0.2 to 14.9lb

C)

–1.0 to 16.1 lb

D)

–0.7to 15.8 lb

Solve the problem.

96)

A variable of two populations has a mean of 44 and a standard deviation of 9 for one of the

populations and a mean of 10 and a standard deviation of 7 for the other population. For

independent samples of sizes 14 and 4, respectively, find the mean of x1–x2.

96)

A)

34

B)

0.6

C)

–34

D)

54

Summary statistics are given for independent simple random samples from two populations. Use the pooled t–test to

conduct the required hypothesis test.

97)

x1=17, s1=4, n1= 10, x2=26, s2=6, n2= 14

Perform a left–tailed hypothesis test using a significance level of  = 0.05.

97)

A)

Test statistic: t = –4.121

Critical value = –1.717

P < 0.005

Reject H0

B)

Test statistic: t = –4.121

Critical value = –2.074

P < 0.005

Reject H0

C)

Test statistic: t = –0.916.916

Critical value = –2.074

P–value > 0.100.100.005

Do not reject H0

D)

Test statistic: t = –1.526526

Critical value = –1.717

0.05 < P < 0.10

Do not reject H0

Use the paired t–interval procedure to obtain the required confidence interval. You may assume that the conditions for

using the procedure are satisfied.

98)

Using the sample paired data below, determine a 90% confidence interval for the difference

between the mean of x and the mean of y.

x4.2 7.2 6.2 4.8 6.5

y3.9 6.0 5.8 5.5 4.2

98)

A)

0.22 to 7.48

B)

–0.37 to 1.77

C)

–0.07 to 1.47

D)

–0.31 to 1.71

Determine the null and alternative hypotheses for the proposed hypothesis test.

99)

A researcher is interested in comparing the resting pulse rate of women who exercise regularly and

women who do not exercise regularly. She wants to perform a hypothesis test to determine

whether the mean resting pulse rate of women who exercise at least 6 hours per week is less than

the mean resting pulse rate of women who exercise less than 6 hours per week.

99)

A)

Let µ1 denote the mean resting pulse rate for women who exercise at least 6 hours per week

and let µ2 denote the mean resting pulse rate for women who exercise less than 6 hours per

week. The null and alternative hypotheses are H0: µ1<µ2 and Ha: µ1>µ2.

B)

Let x1 denote the mean resting pulse rate for women who exercise at least 6 hours per week

and let x2 denote the mean resting pulse rate for women who exercise less than 6 hours per

week. The null and alternative hypotheses are H0: x1=x2 and Ha: x1<x2.

C)

Let µ1 denote the mean resting pulse rate for women who exercise at least 6 hours per week

and let µ2 denote the mean resting pulse rate for women who exercise less than 6 hours per

week. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1>µ2.

D)

Let µ1 denote the mean resting pulse rate for women who exercise at least 6 hours per week

and let µ2 denote the mean resting pulse rate for women who exercise less than 6 hours per

week. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1<µ2.

Summary statistics are given for independent simple random samples from two populations. Use the nonpooled

t–interval procedure to obtain the specified confidence interval.

100)

x1=73.0, s1= 10.9, n1= 16, x2=68.2, s2= 8.2, n2= 12

95% confidence interval

100)

A)

–4.17 to 13.77

B)

–2.64 to 12.24

C)

–1.62 to 11.22

D)

–2.93 to 12.53

Determine the null and alternative hypotheses for the proposed hypothesis test.

101)

A researcher wants to perform a hypothesis test to determine whether the mean length of

marriages in California differs from the mean length of marriages in Texas.

101)

A)

Let x1 denote the mean length of marriages in California and let x2 denote the mean length

of marriages in Texas. The null and alternative hypotheses are H0: x1=x2 and Ha: x1x2.

B)

Let µ1 denote the mean length of marriages in California and let µ2 denote the mean length of

marriages in Texas. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1µ2.

C)

Let µ1 denote the mean length of marriages in California and let µ2 denote the mean length of

marriages in Texas. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1>µ2.

D)

Let µ1 denote the mean length of marriages in California and let µ2 denote the mean length of

marriages in Texas. The null and alternative hypotheses are H0: µ1µ2 and Ha: µ1=µ2.

Solve the problem.

102)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for women is less than the mean forced vital capacity for men. Identify the two populations for the

proposed hypothesis test.

102)

A)

Women with low forced vital capacity and women with high forced vital capacity

B)

Women and men

C)

Forced vital capacity values for women and forced vital capacity values for men

D)

Mean forced vital capacity for women and mean forced vital capacity for men

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

103)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for women is less than the mean forced vital capacity for men.

103)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Provide an appropriate response.

104)

A researcher would like to conduct a hypothesis test to compare the mean SAT scores of students

who have received extra coaching and the mean SAT score of students who have not received extra

coaching. In this case, a paired t–test would be appropriate since a natural pairing exists (a pair

consists of a student before coaching and the same student after coaching). If the researcher instead

uses independent samples and a pooled or nonpooled t–test, how is this likely to affect the

probability of a Type II error?

104)

A)

Using independent samples, the probability of a Type II error is likely to be the same as if a

paired sample were used.

B)

Using independent samples, the probability of a Type II error is likely to be smaller than if a

paired sample is used.

C)

Using independent samples, the probability of a Type II error is likely to be larger than if a

paired sample is used.

A confidence interval (CI) for the difference µ1–µ2 between two population means is given. Interpret the confidence

interval.

105)

90% CI from 207 to 280

105)

A)

We can be 90% confident that µ1–µ2 lies somewhere between 207 and 280. Equivalently, we

can be 90% confident that µ1 is somewhere between 207 and 280 greater than µ2.

B)

We can be 90% confident that µ2–µ1 lies somewhere between 207 and 280. Equivalently, we

can be 90% confident that µ2 is somewhere between 207 and 280 greater than µ1.

C)

We can be 90% confident that µ1 and µ2 both lie somewhere between 207 and 280.

D)

We can be 90% confident that µ1–µ2 lies somewhere between 207 and 280. Equivalently, we

can be 90% confident that µ1 is somewhere between 207 and 280 less than µ2.

Use the paired t–interval procedure to obtain the required confidence interval. You may assume that the conditions for

using the procedure are satisfied.

106)

Ten different families are selected at random. The amount of water each family uses per day before

and after viewing a conservation video is recorded. The amounts (in gallons) are shown below.

Before 33 33 38 33 35 35 40 40 40 31

After 34 28 25 28 35 33 31 28 35 33

Determine a 90% confidence interval for the difference between the mean numbers of gallons of

water used per day before and after viewing the video.

106)

A)

1.5 to 8.1 gallons

B)

3.8 to 5.8 gallons

C)

1.8 to 7.8 gallons

D)

2.5 to 7.1 gallons

Provide an appropriate response.

107)

True or false? In the pooled t–test, sp2 is an estimate of the unknown population variance, 2, and

it is obtained by pooling the sample variances by weighting them by degrees of freedom.

107)

A)

True

B)

False

Apply the pooled t–interval procedure to obtain the required confidence interval. You may assume that the assumptions

for using the procedure are satisfied.

108)

A researcher was interested in comparing the GPAs of students at two different colleges.

Independent simple random samples of 8 students from college A and 13 students from college B

yielded the following GPAs.

College A College B

3.7 3.8 2.8

3.2 3.2 4.0

3.0 3.0 3.6

2.5 3.9 2.6

2.7 3.8 4.0

3.6 2.5 3.6

2.8 3.9

3.4

Determine a 95% confidence interval for the difference between the mean GPA of college A students

and the mean GPA of college B students.

(Note: x1= 3.1125, x2= 3.4385, s1= 0.4357, s2= 0.5485.)

108)

A)

–0.81 to 0.15

B)

–0.91 to 0.25

C)

–0.72 to 0.07

D)

–0.65 to –0.01

50

Provide an appropriate response.

109)

A nutritionist wants to investigate whether her new diet will be effective in helping women aged

30–40 to lose weight. She will use a paired sample to determine whether the mean weight of

women before going on this diet is greater than the mean weight of women after being on this diet

for two months. Identify the pairs for the proposed hypothesis test.

109)

A)

Each pair consists of the mean weight of woman aged 30–40 who are not on this diet and the

mean weight of woman aged 30–40 who have been on this diet for two months.

B)

Each pair consists of a woman aged 30–40 before going on the diet and the same woman after

being on the diet for two months.

C)

Each pair consists of a randomly selected woman aged 30–40 who is not on this diet and a

randomly selected woman aged 30–40 who has been on this diet for two months.

D)

Each pair consists of the weight of a woman aged 30–40 before going on the diet and the

weight of the same woman after being on the diet for two months.

Solve the problem.

110)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for adults who are smokers is less than the mean forced vital capacity for adults who are former

smokers. He will use a paired sample to determine whether forced vital capacity increases, on

average, when adults stop smoking. Identify the variable for the proposed hypothesis test.

110)

A)

Number of cigarettes smoked per day

B)

Forced vital capacity

C)

Difference between mean forced vital capacity of smokers and mean forced vital capacity of

former smokers

D)

Amount of time since person stopped smoking

Determine the null and alternative hypotheses for the proposed hypothesis test.

111)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for women is less than the mean forced vital capacity for men.

111)

A)

Let x1 denote the mean forced vital capacity for women and let x2 denote the mean forced

vital capacity for men. The null and alternative hypotheses are H0: x1=x2 and

Ha: x1<x2.

B)

Let µ1 denote the mean forced vital capacity for women and let µ2 denote the mean forced

vital capacity for men. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1<µ2.

C)

Let µ1 denote the mean forced vital capacity for women and let µ2 denote the mean forced

vital capacity for men. The null and alternative hypotheses are H0: µ1=µ2 and Ha: µ1>µ2.

D)

Let µ1 denote the mean forced vital capacity for women and let µ2 denote the mean forced

vital capacity for men. The null and alternative hypotheses are H0: µ1<µ2 and Ha: µ1>µ2.

Provide an appropriate response.

112)

Suppose that x is a variable on each of two populations. Independent samples of sizes n1 and n2,

respectively, are selected from the two populations. True or false? The mean of all possible

differences between the two sample means equals the difference between the two population

means, regardless of the distributions of the variable on the two populations.

112)

A)

True

B)

False

Solve the problem.

113)

A pharmaceutical company wants to determine whether its new antianxiety medication has any

effect on resting pulse rate. They will use a paired sample to determine whether the mean resting

pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate

for adults who are taking the antianxiety medication. Identify the variable for the proposed

hypothesis test.

113)

A)

Difference between mean resting pulse rate for those not on the medication and the mean

resting pulse rate for those on the medication

B)

Anxiety level

C)

Amount of medication taken

D)

Resting pulse rate

Provide an appropriate response.

114)

A company which designs sports shoes has made an improvement to their popular running shoe.

They hope that athletes wearing the new running shoe will be able to run faster over short

distances. They will use a paired sample to determine whether the mean time to run 100 meters for

sprinters wearing the new running shoe is less than the mean time to run the 100 meters for

sprinters wearing the old running shoe. Identify the paired–difference variable for the proposed

hypothesis test.

114)

A)

Difference between mean time to run 100 meters for sprinters wearing the new running shoe

and mean time to run 100 meters for sprinters wearing the old running shoe

B)

Difference between time to run 100 meters for a sprinter wearing the new running shoe and

time to run 100 meters for the same sprinter after a training period

C)

Difference between time to run 100 meters for a sprinter wearing the new running shoe and

time to run 100 meters for the same sprinter wearing the old running shoe

D)

Difference between time to run 100 meters for a randomly selected sprinter wearing the new

running shoe and time to run 100 meters for a randomly selected sprinter wearing the old

running shoe

Solve the problem.

115)

A researcher is interested in comparing the resting pulse rate of women who exercise regularly and

women who do not exercise regularly. She wants to perform a hypothesis test to determine

whether the mean resting pulse rate of women who exercise at least 6 hours per week is less than

the mean resting pulse rate of women who exercise less than 6 hours per week. Identify the two

populations for the proposed hypothesis test.

115)

A)

Women with a high resting pulse rate and women with a low resting pulse rate

B)

Adults who exercise at least 6 hours per week and adults who exercise less than 6 hours per

week

C)

Women who exercise at least 6 hours per week and women who exercise less than 6 hours per

week

D)

Resting pulse rates for women who exercise at least 6 hours per week and resting pulse rates

for women who exercise less than 6 hours per week

Solve.

116)

A variable of two populations has a mean of 8.4 and a standard deviation of 4.6 for one of the

populations and a mean of 7.3 and a standard deviation of 4.2 for the other population. Determine

the percentage of all pairs of independent samples of sizes 4 and 8, respectively, from the two

populations with the property that the difference x1–x2 between the samples means is between

–3.34 and 5.62.

116)

A)

96.08%

B)

81.71%

C)

87.10%

D)

89.79%

Provide an appropriate response.

117)

Suppose that x is a variable on each of two populations. Independent samples of sizes 5 and 8,

respectively, are selected from the two populations. True or false? x1–x2 is normally distributed,

regardless of the distributions of the variable on the two populations.

117)

A)

True

B)

False

118)

True or false? In the pooled t–test, sp2 is an estimate of the unknown population variance, 2, and

it is obtained by averaging the two sample variances.

118)

A)

True

B)

False

Apply the pooled t–interval procedure to obtain the required confidence interval. You may assume that the assumptions

for using the procedure are satisfied.

119)

A researcher was interested in comparing the salaries of female and male employees at a particular

company. Independent simple random samples of 8 female employees and 15 male employees

yielded the following weekly salaries (in dollars).

Female Male

495 722 518

760 562 904

556 880 1150

904 520 805

520 500 480

1005 1250 970

743 750 605

660 1640

Determine a 98% confidence interval for the difference between the mean weekly salary of female

employees and the mean weekly salary of male employees at this particular company.

(Note: x1= 705.375, x2= 817.067, s1= 183.855, s2= 330.146.)

119)

A)

–$411 to $188

B)

–$431 to $208

C)

–$311 to $88

D)

–$375 to $151

Solve the problem.

120)

A variable of two populations has a mean of 6.9 and a standard deviation of 5.4 for one of the

populations and a mean of 6.7 and a standard deviation of 2.5 for the other population. For

independent samples of sizes 3 and 9, respectively, find the standard deviation of x1–x2. Round

your answer to the nearest hundredth if necessary.

120)

A)

3.44

B)

2.9

C)

11.8

D)

3.95

Summary statistics are given for independent simple random samples from two populations. Preliminary data analyses

indicate that the variable under consideration is normally distributed on each population. Decide whether use of the

pooled t–test and pooled t–interval procedure is reasonable. Explain your answer.

121)

x1= 566.9, s1=51.2, n1= 37, x2= 480.2, s2=53.5, n2= 42

121)

A)

Reasonable; the sample means are close to being equal suggesting that the assumption of

equal population means is reasonable. Also both sample sizes are large.

B)

Not reasonable; the sample means suggest that the two population means differ.

C)

Reasonable; the sample standard deviations are close to being equal suggesting that the

assumption of equal population standard deviations is reasonable. Also both sample sizes are

large.

D)

Not reasonable; the sample standard deviations suggest that the two population standard

deviations differ.

Provide an appropriate response.

122)

Suppose that x is a normally distributed variable on each of two populations. Independent samples

of sizes n1 and n2, respectively, are selected from the two populations. True or false? The standard

deviation of all possible differences between the two sample means equals the square root of the

difference of the population variances each divided by the corresponding sample size.

122)

A)

True

B)

False

B

123)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for adults who are smokers is less than the mean forced vital capacity for adults who are former

smokers. He will use a paired sample to determine whether forced vital capacity increases, on

average, when adults stop smoking. Identify the paired–difference variable for the proposed

hypothesis test.

123)

A)

An adult who smokes and the same person after they stop smoking.

B)

Difference between the mean forced vital capacity of adults who smoke and the mean forced

vital capacity of adults who have stopped smoking.

C)

Difference between the forced vital capacity of a randomly selected adult who smokes and the

forced vital capacity of a randomly selected adult who has stopped smoking.

D)

Difference between the forced vital capacity of an adult who smokes and the forced vital

capacity of the same person after they stop smoking.

D

C

124)

A company which designs sports shoes has made an improvement to their popular running shoe.

They hope that athletes wearing the new running shoe will be able to run faster over short

distances. They will use a paired sample to determine whether the mean time to run 100 meters for

sprinters wearing the new running shoe is less than the mean time to run the 100 meters for

sprinters wearing the old running shoe. Identify the pairs for the proposed hypothesis test.

124)

A)

Each pair consists of a sprinter wearing the new running shoe and the same sprinter after a

training period.

B)

Each pair consists of a randomly selected sprinter wearing the old running shoe and a

randomly selected sprinter wearing the new running shoe.

C)

Each pair consists of a sprinter wearing the old running shoe and the same sprinter wearing

the new running shoe.

D)

Each pair consists of a sprinter wearing the new running shoe and his or her time to run the

100 meters.

125)

A researcher was interested in comparing the resting pulse rates of people who exercise regularly

and people who do not exercise regularly. Independent simple random samples were obtained of

16 people aged 30–40 who do not exercise regularly and 12 people aged 30–40 who do exercise

regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary

statistics were as follows.

Do Not Exercise Do Exercise

x1=72.2 x2=69.1

s1=10.0 s2=8.6

n1= 16 n2= 12

The researcher used a pooled t–interval procedure to obtain a 90% confidence interval for the

difference between the mean pulse rate of people who do not exercise regularly and the mean pulse

rate of people who exercise regularly. The 90% confidence interval was found to be

–3.05 to 9.25 beats per minute . Interpret this confidence interval.

125)

A)

We can be 90% confident that the difference between the sample mean pulse rate of people

who do not exercise regularly and the sample mean pulse rate of people who exercise

regularly is somewhere between –3.05 and 9.25 beats per minute .

B)

There is a 90% chance that the difference between the sample mean pulse rate of people who

do not exercise regularly and the sample mean pulse rate of people who exercise regularly

will lie between –3.05 and 9.25 beats per minute .

C)

There is a 90% chance that the difference between the mean pulse rate of people who do not

exercise regularly and the mean pulse rate of people who exercise regularly will lie between

–3.05 and 9.25 beats per minute .

D)

We can be 90% confident that the difference between the mean pulse rate of people who do

not exercise regularly and the mean pulse rate of people who exercise regularly is

somewhere between –3.05 and 9.25 beats per minute .

126)

Suppose that x is a variable on each of two populations. Independent samples of sizes 125 and 102,

respectively, are selected from the two populations. True or false? x1–x2 is approximately

normally distributed, regardless of the distributions of the variable on the two populations.

126)

A)

True

B)

False

127)

Suppose x is a variable on each of two populations whose members can be paired and that a paired

difference is the difference between the values of the variable x on the members of a pair. True or

false? The mean of the paired differences equals the difference between the two population means.

127)

A)

True

B)

False

B)

Use the paired t–interval procedure to obtain the required confidence interval. You may assume that the conditions for

using the procedure are satisfied.

128)

A coach uses a new technique in training middle distance runners. The times, in seconds, for 9

different athletes to run 800 meters before and after this training are shown below.

Athlete A B C D E F G H I

Before 115.2 120.9 108.0 112.4 107.5 119.1 121.3 110.8 122.3

After 116.0 119.1 105.1 111.9 109.1 115.2 118.5 110.7 120.9

Determine a 99% confidence interval for the difference between the mean time before and after

training.

128)

A)

–0.54 to 2.98 seconds

B)

–0.85 to 3.29 seconds

C)

–0.76 to 3.20 seconds

D)

–0.82 to 3.26 seconds

B)

Solve the problem.

129)

A variable of two populations has a mean of 9.2 and a standard deviation of 2.8 for one of the

populations and a mean of 5.8 and a standard deviation of 4.5 for the other population. For

independent samples of sizes 6 and 9, respectively, find the mean of x1–x2.

129)

A)

3.4

B)

6.4

C)

45.00

D)

–3.4

B)

Apply the pooled t–interval procedure to obtain the required confidence interval. You may assume that the assumptions

for using the procedure are satisfied.

130)

A researcher was interested in comparing the amount of time spent watching television by women

and by men. Independent simple random samples of 14 women and 17 men were selected and

each person was asked how many hours he or she had watched television during the previous

week. The summary statistics are as follows.

Women Men

x1=12.5 x2=17.7

s1=4.3 s2=4.5

n1= 14 n2= 17

Determine a 95% confidence interval for the difference between the mean weekly television

watching times of women and men.

130)

A)

–7.91 to –2.49 hours

B)

–8.46 to –1.94 hours

C)

–8.73 to –1.67 hours

D)

–8.57 to –1.83 hours

Apply the nonpooled t–interval procedure to obtain the required confidence interval. You may assume that the

assumptions for using the procedure are satisfied.

131)

A researcher was interested in comparing the resting pulse rates of people who exercise regularly

and people who do not exercise regularly. Independent simple random samples of 16 people ages

30–40 who do not exercise regularly and 12 people ages 30–40 who do exercise regularly were

selected, and the resting pulse rate (in beats per minute) of each person was measured. The

summary statistics are as follows.

Do Not Exercise Do Exercise

x1=72.9 x2=69.6

s1= 10.9 s2= 8.2

n1= 16 n2= 12

Determine a 95% confidence interval for the difference, µ1–µ2, between the mean pulse rate of

people who do not exercise and the mean pulse rate of people who do exercise.

131)

A)

–4.14 to 10.74 beats per minute

B)

–4.43 to 11.03 beats per minute

C)

–5.67 to 12.27 beats per minute

D)

–3.12 to 9.72 beats per minute

Summary statistics are given for independent simple random samples from two populations. Preliminary data analyses

indicate that the variable under consideration is normally distributed on each population. Decide whether use of the

pooled t–test and pooled t–interval procedure is reasonable. Explain your answer.

132)

x1= 143.9, s1= 16.2, n1= 7, x2= 212.9, s2= 46.7, n2= 17

132)

A)

Reasonable; the sample standard deviations suggest that the two population standard

deviations are equal.

B)

Not reasonable; the sample standard deviations suggest that the two population standard

deviations are equal, however since the sample sizes are not roughly equal, it is not

reasonable to use the pooled t–test.

C)

Not reasonable; the sample standard deviations suggest that the two population standard

deviations differ and the sample sizes are not roughly equal.

D)

Reasonable; the sample standard deviations suggest that the two population standard

deviations differ, however since the sample sizes are roughly equal, it is reasonable to use the

pooled t–test.

Apply the pooled t–interval procedure to obtain the required confidence interval. You may assume that the assumptions

for using the procedure are satisfied.

133)

A paint manufacturer wanted to compare the drying times of two different types of paint.

Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and

applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are

as follows.

Type A Type B

x1=71.6 x2=68.3

s1=3.3 s2=3.2

n1= 11 n2= 9

Determine a 99% confidence interval for the difference between the mean drying time of type A

and the mean drying time of type B.

133)

A)

–0.91 to 7.51 hours

B)

–1.58 to 8.18 hours

C)

–0.43 to 7.03 hours

D)

0.37 to 6.23 hours

Summary statistics are given for independent simple random samples from two populations. Use the pooled t–test to

conduct the required hypothesis test.

134)

x1=12.4, s1=4.3, n1= 14, x2=17.2, s2=4.4, n2= 17

Perform a two–tailed hypothesis test using a significance level of  = 0.05.

134)

A)

Test statistic: t = –1.841

Critical value = ±1.699

Reject H0

B)

Test statistic: t = –3.054

Critical value = ±2.045

Reject H0

C)

Test statistic: t = –3.054

Critical value = ±1.699

Do not reject H0

D)

Test statistic: t = –1.841

Critical value = ±2.045

Do not reject H0

Classify the proposed hypothesis test as Two tailed, Left tailed, or Right tailed.

135)

A researcher wants to use a paired sample to determine whether the mean number of hours spent

exercising per week for married men differs from the mean number of hours spent exercising per

week for married women.

135)

A)

Two tailed

B)

Left tailed

C)

Right tailed

Solve the problem.

136)

The forced vital capacity (FVC) is often used by physicians to assess a person’s ability to move air in

and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A

researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity

for adults who are smokers is less than the mean forced vital capacity for adults who are former

smokers. He will use a paired sample to determine whether forced vital capacity increases, on

average, when adults stop smoking. Identify the two populations for the proposed hypothesis test.

136)

A)

Adults who smoke and adults who are former smokers

B)

Adults with a high forced vital capacity and adults with a low forced vital capacity

C)

Smokers with a high forced vital capacity and smokers with a low forced vital capacity

D)

Adults who smoke and adults who don’t smoke

Summary statistics are given for independent simple random samples from two populations. Use the nonpooled t–test to

conduct the required hypothesis test.

137)

x1=12.5, s1= 3.9, n1= 14, x2=13.5, s2= 5.2, n2= 17

Perform a left–tailed hypothesis test using a significance level of  = 0.05.

137)

A)

Test statistic: t = –0.611

Critical value = –1.699

Do not reject H0

B)

Test statistic: t = –2.211

Critical value = –1.699

Reject H0

C)

Test statistic: t = –0.611

Critical value = –1.701

Do not reject H0

D)

Test statistic: t = –2.211

Critical value = –1.701

Reject H0

Provide an appropriate response.

138)

A researcher wants to use a paired sample to determine whether the mean number of hours spent

exercising per week for married men differs from the mean number of hours spent exercising per

week for married women. Identify the paired–difference variable for the proposed hypothesis test.

138)

A)

Difference between hours of weekly exercise for a married man and hours of weekly exercise

before he was married

B)

Difference between hours of weekly exercise for a married man and hours of weekly exercise

of his wife

C)

Difference between mean hours of weekly exercise of married men and mean hours of weekly

exercise of married women

D)

Difference between hours of weekly exercise of a randomly selected married man and hours

of weekly exercise of a randomly selected married woman

139)

A nutritionist wants to investigate whether her new diet will be effective in helping women aged

30–40 to lose weight. She will use a paired sample to determine whether the mean weight of

women before going on this diet is greater than the mean weight of women after being on this diet

for two months. Identify the paired–difference variable for the proposed hypothesis test.

139)

A)

Difference between weight of a randomly selected woman aged 30–40 who is not on this diet

and weight of a randomly selected woman aged 30–40 who has been on this diet for two

months.

B)

Difference between mean weight of women aged 30–40 who are not on this diet and mean

weight of women aged 30–40 who have been on this diet for two months.

C)

Difference between weight of a woman aged 30–40 after being on this diet for two months

and weight of her husband after being on this diet for two months.

D)

Difference between weight of a woman aged 30–40 before going on this diet and weight of

same woman after being on this diet for two months.

Solve the problem.

140)

A researcher wants to use a paired sample to determine whether the mean number of hours spent

exercising per week for married men differs from the mean number of hours spent exercising per

week for married women. Identify the variable for the proposed hypothesis test.

140)

A)

Difference between mean hours of exercise per week for married men and mean hours of

exercise per week for married women

B)

Hours of exercise per week

C)

Marital status

D)

Gender

Summary statistics are given for independent simple random samples from two populations. Use the pooled t–test to

conduct the required hypothesis test.

141)

x1=16, s1=6, n1= 12, x2=14, s2=8, n2= 15

Perform a right–tailed hypothesis test using a significance level of  = 0.05.

141)

A)

Test statistic: t =6.667

Critical value = 2.060

P–value < 0.0050.005

Reject H0

B)

Test statistic: t =0.718

Critical value = 2.060

P–value > 0.10

Do not reject H0

C)

Test statistic: t =0.718

Critical value = 1.708

P–value > 0.10

Do not reject H0

D)

Test statistic: t =6.667

Critical value = 1.708

P–value < 0.0050.005

Reject H0

Summary statistics are given for independent simple random samples from two populations. Use the pooled t–interval

procedure to obtain the specified confidence interval.

142)

x1=11.2, s1=4.4, n1= 14, x2=17.5, s2=4.9, n2= 17

Determine a 95% confidence interval.

142)

A)

–10.05 to –2.55

B)

–9.88 to –2.72

C)

–9.76 to –2.84

D)

–9.17 to –3.43

Solve the problem.

143)

A researcher wants to use a paired sample to determine whether the mean number of hours spent

exercising per week for married men differs from the mean number of hours spent exercising per

week for married women. Identify the two populations for the proposed hypothesis test.

143)

A)

Married people and single people

B)

Married men and married women

C)

Married people who exercise and married people who don‘t exercise

D)

Men and women

Provide an appropriate response.

144)

A pharmaceutical company wants to determine whether its new antianxiety medication has any

effect on resting pulse rate. They will use a paired sample to determine whether the mean resting

pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate

for adults who are taking the antianxiety medication. Identify the paired–difference variable for the

proposed hypothesis test.

144)

A)

Difference between mean resting pulse rate of adults not on the antianxiety medication and

the mean resting pulse rate of adults on the antianxiety medication

B)

Difference between resting pulse rate of a randomly selected adult who is not on the

antianxiety medication and the resting pulse rate of a randomly selected adult on the

antianxiety medication

C)

Difference between resting pulse rate of an adult on the medication and the pulse rate of the

same person after exercising

D)

Difference between resting pulse rate of an adult who is not on the antianxiety medication

and the resting pulse rate of the same person on the antianxiety medication

Summary statistics are given for independent simple random samples from two populations. Preliminary data analyses

indicate that the variable under consideration is normally distributed on each population. Decide whether use of the

pooled t–test and pooled t–interval procedure is reasonable. Explain your answer.

145)

x1= 143.9, s1= 42.2, n1= 13, x2= 212.9, s2= 152.7, n2= 15

145)

A)

Not reasonable; the sample standard deviations suggest that the two population standard

deviations differ.

B)

Not reasonable; the sample means suggest that the two population means differ.

C)

Reasonable; the sample standard deviations suggest that the two population standard

deviations differ, however since the sample sizes are roughly equal, it is reasonable to use the

pooled t–test.

D)

Reasonable; the sample standard deviations suggest that the two population standard

deviations are equal.

Use the paired t–interval procedure to obtain the required confidence interval. You may assume that the conditions for

using the procedure are satisfied.

146)

A test of writing ability is given to a random sample of students before and after completing a

formal writing course. The results are shown below.

Before 70 80 92 99 93 97 76 63 68 71 74

After 69 79 90 96 91 95 75 64 62 64 76

Determine a 99% confidence interval for the difference between the mean score before and after

completing the writing course.

146)

A)

–0.1 to 4.1

B)

1.2 to 2.8

C)

–0.2 to 4.2

D)

–0.5 to 4.5

D

Summary statistics are given for independent simple random samples from two populations. Use the nonpooled t–test to

conduct the required hypothesis test.

147)

x1=74.0, s1= 4.5, n1= 11, x2=66.9, s2= 5.1, n2= 9

Perform a two–tailed hypothesis test using a significance level of  = 0.01.

147)

A)

Test statistic: t = 2.646

Critical values = ±2.921

Do not reject H0

B)

Test statistic: t = 2.646

Critical values = ±2.878

Do not reject H0

C)

Test statistic: t =3.264

Critical values = ±2.921

Reject H0

D)

Test statistic: t =3.264

Critical values = ±2.878

Reject H0

C

A

Determine the null and alternative hypotheses for the proposed hypothesis test.

148)

A researcher wants to perform a hypothesis test to determine whether the mean credit card debt for

credit card holders aged 18–35 is greater than the mean credit card debt for credit card holders aged

over 35.

148)

A)

Let µ1 denote the mean credit card debt for credit card holders aged 18–35 and let µ2 denote

the mean credit card debt for credit card holders over 35. The null and alternative hypotheses

are H0: µ1=µ2 and Ha: µ1>µ2.

B)

Let µ1 denote the mean credit card debt for credit card holders aged 18–35 and let µ2 denote

the mean credit card debt for credit card holders over 35. The null and alternative hypotheses

are H0: µ1>µ2 and Ha: µ1<µ2.

C)

Let x1 denote the mean credit card debt for credit card holders aged 18–35 and let x2 denote

the mean credit card debt for credit card holders over 35. The null and alternative hypotheses

are H0: x1=x2 and Ha: x1>x2.

D)

Let µ1 denote the mean credit card debt for credit card holders aged 18–35 and let µ2 denote

the mean credit card debt for credit card holders over 35. The null and alternative hypotheses

are H0: µ1=µ2 and Ha: µ1<µ2.

Answer Key

Testname: C10

67

Answer Key

Testname: C10

Answer Key

Testname: C10

Answer Key

Testname: C10

70

Answer Key

Testname: C10

Answer Key

Testname: C10

Answer Key

Testname: C10

Answer Key

Testname: C10