Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
Suppose that you want to perform a hypothesis test to compare the means of two populations
using independent simple random samples. In which of the situations below is it reasonable to use
the Mann–Whitney test?
1)
A)
The distributions of the variable are normal, and the population standard deviations are not
equal.
B)
The distributions of the variable are not normal, and they do not have the same shape.
C)
The distributions of the variable are not normal, and they have the same shape.
D)
A and B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable to
apply the z–test. Use the critical–value approach.
2)
A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets
have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the
2% level of significance. The mean acetaminophen content for a random sample of n =50
tablets is 603.3 mg. Assume that the population standard deviation is 5 mg.
2)
1
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.
3)
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.
3)
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: µ1µ2.
4)
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.
4)
A)
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: x1x2.
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: µ1µ2.
C)
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.
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: µ1µ2 and Ha: µ1=µ2.
2
5)
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.
5)
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: µ1µ2.
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.
6)
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?
6)
A)
The difference between the two population means
B)
The sum of the two population means
C)
The difference between the two sample means
D)
The sum of the two sample means
3
7)
Which of the following statements regarding the equal–standard–deviations assumption of the
pooled t–test is the most accurate?
7)
A)
The pooled t–test is robust to moderate violations of the assumption provided the sample
sizes are roughly equal.
B)
The pooled t–test is robust to moderate violations of the assumption provided the sample
sizes are large.
C)
The pooled t–test is robust to moderate violations of the assumption regardless of the sample
sizes.
D)
The pooled t–test is extremely nonrobust to violations of the assumption.
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
4
Determine the null and alternative hypotheses for the proposed hypothesis test.
9)
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.
9)
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.
5
10)
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.
10)
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: µ1µ2 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: x1x2.
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: µ1µ2.
6
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
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.
11)
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.
11)
Provide an appropriate response.
12)
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.
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 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.)
13)
Provide an appropriate response.
14)
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.
14)
15)
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.
15)
16)
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.
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)
Five students took a math test before and after tutoring. Their scores were as follows.
Subject A B C D E
Before 75 73 75 73 75
After 79 82 73 76 87
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.
17)
9
Provide an appropriate response.
18)
Suppose that you want to perform a hypothesis test based on independent simple random
samples to compare the means of two populations. Assume that the variable under
consideration is skewed to the right on both populations , that the two population standard
deviations are equal, and that the sample sizes are large. Identify the procedures that could
be used to carry out the hypothesis test, that is, the procedures whose assumptions are
satisfied. If more than one procedure could be used, which one would be the best? Explain
your answer.
18)
Preliminary data analyses indicates that use of a paired Wilcoxon signed–rank test is reasonable. Perform the hypothesis
test by using a paired Wilcoxon signed–rank test. Assume that the null hypothesis is H0 : µ1=µ2.
19)
The systolic blood pressure readings of ten subjects before and after following a particular
diet for a month are shown in the following table.
Subject Before After
A 175 162
B 192 190
C 167 170
D 180 180
E 161 153
F 203 197
G 185 191
H 176 174
I 204 192
J 146 150
At the 1% level of significance, do the data provide sufficient evidence to conclude that the
diet has an effect on systolic blood pressure?
19)
10
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.
20)
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 112.5 109.2 111.9 116.1 110.9 113.9 112.5 113.2
After 113.1 107.9 109.5 116.9 109.1 114 108.9 109.3
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.
20)
21)
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 188 163 191 154 187 174 179
After 181 154 189 159 173 176 167
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.
21)
Explanation:
Provide an appropriate response.
22)
Suppose that you want to perform a hypothesis test based on independent simple random
samples to compare the means of two populations. Assume that the variable under
consideration is uniformly distributed on both of the populations and that the two
population standard deviations are equal. Both sample sizes are small. Identify the
procedures that could be used to carry out the hypothesis test, that is, the procedures
whose assumptions are satisfied. If more than one procedure could be used, which one
would be the best? Explain your answer.
22)
Explanation:
Explanation:
23)
Suppose that you want to perform a hypothesis test based on a simple random paired
sample to compare the means of two populations. Assume that the paired–difference
variable has a symmetric bimodal distribution and that the sample size is 40. Identify the
procedures that could be used to carry out the hypothesis test, that is, the procedures
whose assumptions are satisfied. If more than one procedure could be used, which one
would be the best? Explain your answer.
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 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=12.4 x2=14.2
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.
24)
12
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.
25)
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 9.5 9.7 9.7 9.4 9.4 9.5 9.5
After 9.6 9.9 9.7 9.3 9.5 9.8 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 P–value approach.
25)
26)
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 9.6 9.5 9.4 9.7 9.5 9.4 9.5
After 9.7 9.7 9.4 9.6 9.6 9.7 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.
26)
13
Provide an appropriate response.
27)
Suppose that you want to perform a hypothesis test based on independent simple random
samples to compare the means of two populations. Normal probability plots for the two
samples are linear and therefore suggest that the variable under consideration is normally
distributed on each population. Is it then reasonable to proceed with a pooled t–test? If not,
what additional information is required and what methods might be used to obtain this
information?
27)
Preliminary data analyses indicate that you can reasonably consider the assumptions for using the Mann–Whitney test
satisfied. Assume that the null hypothesis is H0: µ1=µ2. Use the Mann–Whitney test to carry out the required
hypothesis test.
28)
A researcher was interested in investigating how much people read in their spare time and,
in particular, whether people who own a personal computer read less in their spare time
than those who do not own a computer. She selected independent simple random samples
of 7 computer owners and 9 noncomputer owners, and she asked each person how many
hours he or she had spent reading non–work–related books during the previous week. The
results are as follows.
Computer Owners Noncomputer Owners
1.7 1.8
06.6
2.6 0.3
0.9 0
6.2 4.2
02.3
0.5 8.8
2.2
1.4
At the 2.5% significance level, do the data provide sufficient evidence to conclude that the
mean weekly reading time for computer owners is lower than the mean weekly reading
time for noncomputer owners?
28)
14
Provide an appropriate response.
29)
Students take a math test before and after tutoring. The data for a random sample of
students is given below.
Before 54 72 63 82 51 80 63 36 44
After 68 70 67 78 55 83 63 52 40
Suppose that you want to use these data to perform a hypothesis test to determine whether
the mean score before the tutoring is lower than the mean score after the tutoring. Conduct
preliminary graphical data analyses to decide whether it is reasonable to apply the paired
t–test and whether it is reasonable to apply the paired Wilcoxon signed–rank test or
whether neither test is reasonable. If both tests are reasonable,which test would be
preferable? Explain your thinking.
29)
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.
30)
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.
30)
Provide an appropriate response.
31)
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.
31)
15
Preliminary data analyses indicate that you can reasonably consider the assumptions for using the Mann–Whitney test
satisfied. Assume that the null hypothesis is H0: µ1=µ2. Use the Mann–Whitney test to carry out the required
hypothesis test.
32)
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 2.5% significance level, do the data provide sufficient evidence to conclude that
women in country A are, on average, taller than women in country B?
32)
Provide an appropriate response.
33)
Suppose that you want to perform a hypothesis test to compare the means of two
populations. Several procedures are available, namely, the pooled t–test, the nonpooled
t–test, the Mann–Whitney test, the paired t–test, and the Wilcoxon signed–rank test. Before
selecting the appropriate procedure, you need to look at the sample data to ascertain
distribution type. What methods are available for doing this?
33)
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.
34)
Five students took a math test before and after tutoring. Their scores were as follows.
Subject A B C D E
Before 73 66 76 69 72
After 77 75 74 72 84
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.
34)
Provide an appropriate response.
35)
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.
35)
36)
Suppose that you want to perform a hypothesis test based on independent simple random
samples to compare the means of two populations. Assume that the variable under
consideration is uniformly distributed on one of the populations and that on the other
population it is skewed to the right. Both sample sizes are large. Identify the procedures
that could be used to carry out the hypothesis test, that is, the procedures whose
assumptions are satisfied. If more than one procedure could be used, which one would be
the best? Explain your answer.
36)
17
37)
A statistician performs a Mann–Whitney test to compare the means of two populations
using independent simple random samples. Suppose that the sum of the ranks for sample
1 is much larger than the sum of the ranks for sample 2. Explain in your own words what
this suggests about the relationship between µ1 and µ2.
37)
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.
38)
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.)
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)
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 168 171 194 182 189 185 158
After 161 162 192 187 175 187 146
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.
39)
Preliminary data analyses indicates that use of a paired Wilcoxon signed–rank test is reasonable. Perform the hypothesis
test by using a paired Wilcoxon signed–rank test. Assume that the null hypothesis is H0 : µ1=µ2.
40)
In a study of the effectiveness of physical exercise in weight reduction, 12 subjects followed
a program of physical exercise for two months. Their weights (in pounds) before and after
this program are shown in the following table.
Before 162 190 188 152 148 127 195 164 175 156 180 136
After 157 194 179 149 135 130 183 168 168 148 170 138
At the 5% significance level, do the data provide sufficient evidence to conclude that the
exercise program is effective in reducing weight?
40)
19
Provide an appropriate response.
41)
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.
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 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.)
42)