Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1)
A high school biology student wishes to test the hypothesis that hummingbird feeders can affect
the mean mass of ruby–throated hummingbirds in the area surrounding the feeder. She captures
and weighs several of the hummingbirds near a science museum where several feeders are located.
She obtains the following masses in grams:
4.2 3.9 3.6 3.5 3.9 3.8
3.8 4.1 3.9 3.8 3.2 3.4
The student’s hypotheses are:
H0: µ= 3.65 g
Ha: µ> 3.65 g
Use technology to calculate the P–value, then determine whether the data provide sufficient
evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater
than the mean mass of the general population. Test at the 5% significance level and assume that the
population standard deviation is 0.35 g. Also, assess the strength of the evidence against the null
hypothesis.
1)
A)
P = 0.745; since P >0.05, do not reject the null hypothesis.
At the 5% significance level, the data do not provide sufficient evidence to conclude that the
mean mass of the birds in the area surrounding the feeder is greater than the mean mass of
the general population. The evidence against the null hypothesis is weak or none.
B)
P = 0.509; since P >0.05, reject the null hypothesis.
At the 5% significance level, the data do provide sufficient evidence to conclude that the mean
mass of the birds in the area surrounding the feeder is greater than the mean mass of the
general population. The evidence against the null hypothesis is strong.
C)
P = 0.1418; since P >0.05, do not reject the null hypothesis.
At the 5% significance level, the data do not provide sufficient evidence to conclude that the
mean mass of the birds in the area surrounding the feeder is greater than the mean mass of
the general population. The evidence against the null hypothesis is weak or none.
D)
P = 0.255; since P >0.05, reject the null hypothesis.
At the 5% significance level, the data do provide sufficient evidence to conclude that the mean
mass of the birds in the area surrounding the feeder is greater than the mean mass of the
general population. The evidence against the null hypothesis is moderate.
2)
A high school biology student wishes to test the hypothesis that hummingbird feeders can affect
the mean mass of ruby–throated hummingbirds in the area surrounding the feeder. She captures
and weighs several of the hummingbirds near a science museum where several feeders are located.
She obtains the following masses in grams:
4.4 3.9 4.5 4.3 4.1 3.8
3.8 4.1 3.9 3.8 3.2 4.3
The student’s hypotheses are:
H0: µ= 3.65 g
Ha: µ> 3.65 g
Use technology to calculate the P–value, then determine whether the data provide sufficient
evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater
than the mean mass of the general population. Test at the 5% significance level and assume that the
population standard deviation is 0.35 g. Also, assess the strength of the evidence against the null
hypothesis.
2)
A)
P = 0.9998; since P >0.05, do not reject the null hypothesis.
At the 5% significance level, the data do not provide sufficient evidence to conclude that the
mean mass of the birds in the area surrounding the feeder is greater than the mean mass of
the general population. The evidence against the null hypothesis is weak or none.
B)
P = 0.0004; since P <0.05, do not reject the null hypothesis.
At the 5% significance level, the data do not provide sufficient evidence to conclude that the
mean mass of the birds in the area surrounding the feeder is greater than the mean mass of
the general population. The evidence against the null hypothesis is weak or none.
C)
P = 0.0002; since P <0.05, reject the null hypothesis.
At the 5% significance level, the data do provide sufficient evidence to conclude that the mean
mass of the birds in the area surrounding the feeder is greater than the mean mass of the
general population. The evidence against the null hypothesis is very strong.
D)
P = 0.0004; since P <0.05, reject the null hypothesis.
At the 5% significance level, the data do provide sufficient evidence to conclude that the mean
mass of the birds in the area surrounding the feeder is greater than the mean mass of the
general population. The evidence against the null hypothesis is very strong.
Solve the problem. Use the critical–value approach.
2
3)
A machine that fills soda bottles is supposed to fill them to a mean volume of 16.2 fluid ounces. A
random sample of 20 filled bottles produced the following volumes in fluid ounces:
16.3 15.9 16.7 15.3 17.1 16.4 3.9 15.9 16.2 3.4
16.4 8.2 15.5 16.5 16.0 16.3 15.8 16.7 16.5 15.5
These data are summarized on the following histogram:
Using technology, perform the following hypothesis test: at the 5% significance level, determine
whether the fill volume is less than the supposed value. Comment on the appropriateness of the
test.
3)
A)
Test statistic: t = –1.8063; Critical value: –1.7254.
Since the test statistic is less than the critical value, do not reject the null hypothesis H0: µ=
16.2 oz.
There is insufficient evidence to conclude that the fill volume is below 16.2 oz. However, the
data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
B)
Test statistic: t = –1.8063; Critical value: –2.0921.
Since the test statistic is greater than the critical value, do not reject the null hypothesis
H0: µ= 16.2 oz. There is insufficient evidence to conclude that the fill volume is below 16.2
oz. The conclusion is on sound statistical ground.
C)
Test statistic: t = –1.8063; Critical value: –1.729.
Since the test statistic is less than the critical value, reject the null hypothesis H0: µ= 16.2 oz.
There is sufficient evidence to conclude that the fill volume is below 16.2 oz. However, the
data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
D)
Test statistic: t = –1.8063; Critical value: –2.0921.
Since the test statistic is greater than the critical value, do not reject the null hypothesis
H0: µ= 16.2 oz. There is insufficient evidence to conclude that the fill volume is below 16.2
oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the
conclusion.
Provide an appropriate response.
4)
Traditionally in hypothesis testing the null hypothesis represents the “status quo” which will be
overturned only if there is evidence against it. Which of the statements below might represent a
null hypothesis?
4)
A)
The defendant is guilty.
B)
The teaching method raises SAT scores.
C)
The treatment has no effect.
D)
None of the above
Solve the problem. Use the critical–value approach.
5)
A sheet–metal press stamps out bolt washers with a nominal inner diameter of 0.25 inches.
Measurement of the inner diameters of a random sample of 14 washers produced the following
results (in inches): 0.253 0.251 0.253 0.251 0.264 0.252 0.259
0.252 0.264 0.263 0.253 0.268 0.266 0.268
The normal scores of the data are summarized below:
Using technology, perform the following hypothesis test: at the 1% significance level, determine
whether the mean washer diameter for this machine exceeds the nominal value. Comment on the
appropriateness of the test.
5)
A)
Test statistic: t = 2.6503; Critical value: 4.5865.
Since the test statistic is less than the critical value, do not reject the null hypothesis
H0: µ= 0.25 inches. There is insufficient evidence to conclude that the inner diameter is larger
than the nominal value. The normal probability distribution plot indicates that the t–test is an
appropriate test.
B)
Test statistic: t = 2.6503; Critical value: 4.5865.
Since the test statistic is less than the critical value, do not reject the null hypothesis
H0: µ= 0.25 inches. There is insufficient evidence to conclude that the inner diameter is larger
than the nominal value. However, the normal probability plot indicates that the data are not
distributed normally, so the t–test may not be appropriate.
4
C)
Test statistic: t = 4.5865; Critical value: 1.7709.
Since the test statistic is greater than the critical value, reject the null hypothesis H0: µ= 0.25
inches.
There is sufficient evidence to conclude that the inner diameter is larger than the nominal
value. However, the normal probability plot indicates that the data are not distributed
normally, so the t–test may not be appropriate.
D)
Test statistic: t = 4.5865; Critical value: 2.650.
Since the test statistic is greater than the critical value, reject the null hypothesis H0: µ= 0.25
inches.
There is sufficient evidence to conclude that the inner diameter is larger than the nominal
value. However, the normal probability plot indicates that the data are not distributed
normally, so the t–test may not be appropriate.
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.
6)
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 =46
tablets is 604.7 mg. Assume that the population standard deviation is 5 mg.
6)
Construct a graph portraying the decision criterion for the specified hypothesis test.
7)
A hypothesis test for a population mean is conducted. The hypotheses are:
H0: µ=µ0
Ha: µ>µ0
The significance level is 0.04 and the critical value is 1.75. Sketch a normal curve
displaying the decision criterion. This curve will represent the normal curve for the test
statistic under the assumption that the null hypothesis is true. On your graph indicate the
area in the tail, the critical value, the rejection region, and the nonrejection region.
7)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
8)
A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A
retailer suspects that the mean weight is actually less than 30 g. The mean weight for a
random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. At the 5%
significance level, test the claim that the mean is less than 30 g.
8)
Provide an appropriate response.
9)
In 1995, the mean math SAT score for students at one school was 488. A teacher introduces
a new teaching method to prepare students for the SAT. One year later, he performs a
hypothesis test to determine whether the mean math SAT score has increased. The
hypotheses are
H0: µ= 488
Ha: µ> 488.
If the null hypothesis is rejected at the 10% level of significance, do you think the teacher
would feel confident that his teaching method works? What about if the null hypothesis is
rejected at the 1% level of significance? Which of these two results would constitute
stronger evidence that his teaching method works? Explain your thinking.
9)
Decide whether it appears reasonable to use a t–test to perform a hypothesis test for the mean in question. Explain your
answer and include any relevant graphs, such as a normal probability plot, histogram, or stem–and–leaf diagram. If there
are outliers, explain how to proceed.
10)
Test scores for a random sample of 12 students were as follows:
22 30 34 37 40 45
49 53 58 65 74 87
10)
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.
11)
A car insurance company has determined that the mean annual car insurance cost for a
family in the town of Watlington is $1716. A researcher wants to perform a hypothesis test
to determine whether the mean insurance cost for a family in the town of Putford is higher
than this. The mean insurance cost for a random sample of 32 families in Putford was
$1761. At the 10% significance level, do the data provide sufficient evidence to conclude
that the mean insurance cost for a family in Putford is higher than $1716, the mean cost for
a family in Watlington.? Assume that the population standard deviation is $35.50.
11)
Provide an appropriate response.
12)
A hypothesis test for a population mean is to be performed. The population standard
deviation is known. The hypotheses are
H0: µ= 80
Ha: µ 80.
A 99% confidence interval will also be constructed for µ. Complete the following statement
concerning the relationship between the hypothesis test and the confidence interval. If 80
lies ___ (within/outside) the 99% confidence interval for µ, then the null hypothesis will be
rejected at the ____ level of significance.
12)
Perform a one–sample z–test for a population mean using the P–value approach. Be sure to state the hypotheses and the
significance level, to compute the value of the test statistic, to obtain the P–value, and to state your conclusion. Also,
assess the strength of the evidence against the null hypothesis.
13)
In one city, the average amount of time that tenth–graders spend watching television each
week is 21.6 hours. The principal of Birchwood High School believes that at his school,
tenth–graders watch less television. For a sample of 28 tenth–graders from Birchwood
High School, the mean amount of time spent watching television per week was 19.4 hours.
Do the data provide sufficient evidence to conclude that for tenth–graders at Birchwood
High School, the mean amount of time spent watching television per week is less than the
city average of 21.6 hours? Perform the appropriate hypothesis test using a significance
level of 5%. Assume that = 7.2 hours.
13)
Two graphical displays are given for a set of data. A hypothesis test is to be performed for the mean of the population
from which the data were obtained. Would it be reasonable to use a one–mean z–test? Explain your reasoning. Assume
that the population standard deviation is known.
14)
A normal probability plot and a stem–and–leaf diagram of the data are given below.
14)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
15)
A large software company gives job applicants a test of programming ability and the mean
for that test has been 160 in the past. Twenty–five job applicants are randomly selected
from a large university and they produce a mean score of 183 with a standard deviation of
12. Use a 0.05 level of significance to test whether the mean score for students from this
university is greater than 160.
15)
16)
In tests of a computer component, it is found that the mean time between failures is
520 hours. A modification is made which is supposed to increase the time between failures.
Tests on a random sample of 10 modified components resulted in the following times (in
hours) between failures.
518 548 561 523 536
499 538 557 528 563
At the 0.05 significance level, test the claim that for the modified components, the mean
time between failures is greater than 520 hours.
16)
Provide an appropriate response.
17)
A hypothesis test for a population mean is to be performed. Suppose that the sample size is
50 but that the data contain outliers. Is it reasonable to use the z–test? How should you
proceed?
17)
18)
A pharmaceutical company has a new drug which relieves headaches. However, there is
some indication that the drug may have the side effect of increasing blood pressure.
Suppose the drug company conducts a hypothesis test to determine whether the
medication raises blood pressure. The hypotheses are:
H0: The drug does not increase blood pressure.
Ha: The drug increases blood pressure.
Do you think that for doctors and patients it is more important to have a small
probability or a small probability? Why? Do you think that the pharmaceutical company
would prefer to have a small probability or a small probability? Why?
18)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
19)
A test of sobriety involves measuring a subject’s motor skills. The mean score for men who
are sober is known to be 35.0. A researcher would like to perform a hypothesis test to
determine whether the mean score for sober women differs from 35.0. Twenty randomly
selected sober women take the test and produce a mean score of 41.0 with a standard
deviation of 3.7. Perform the hypothesis test at the 0.01 level of significance.
19)
Construct a graph portraying the decision criterion for the specified hypothesis test.
20)
A hypothesis test for a population mean is conducted. The hypotheses are:
H0: µ=µ0
Ha: µµ0
The significance level is 0.06 and the critical values are –1.88 and 1.88. Sketch a normal
curve displaying the decision criterion. This curve will represent the normal curve for the
test statistic under the assumption that the null hypothesis is true. On your graph indicate
the area in each tail, the critical values, the rejection region, and the nonrejection region.
20)
Provide an appropriate response.
21)
Give an example of a hypothesis test for which it is important to have a small probability.
Explain why it is important to have a small value for .
21)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
22)
DuraBurn claims that the mean lifetime of its SuperGlo light bulbs is 904 hours. A
researcher wants to perform a hypothesis test to determine whether the mean lifetime is
actually less than this. A random sample of 10 DuraBurn SuperGlo bulbs exhibited an
average lifetime x=810 hours with a standard deviation s =158 hours. Using the
hypotheses
H0: µ=904
Ha: µ<904,
compute the value of the test statistic, and find the P–value for the sample. State your
conclusion. Use a significance level of 0.05.
22)
Two graphical displays are given for a set of data. A hypothesis test is to be performed for the mean of the population
from which the data were obtained. Would it be reasonable to use a one–mean z–test? Explain your reasoning. Assume
that the population standard deviation is known.
23)
A normal probability plot and a histogram plot of the data are given below.
23)
Provide an appropriate response.
24)
Suppose that you wish to perform a hypothesis test for a population mean using the
P–value method. Suppose that the population standard deviation is unknown. The correct
procedure to use is the t–test. If you mistakenly use the standard normal table to obtain the
P–value, will the value that you obtain be larger or smaller than the correct value? Does
the mistaken use of the normal table make it more or less likely that the null hypothesis
will be rejected?
24)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
25)
A test of sobriety involves measuring the subject‘s motor skills. The mean score for men
who are sober is known to be 35.0. A researcher would like to perform a hypothesis test to
determine whether the mean score for sober women differs from 35.0. Twenty randomly
selected sober women take the test and produce a mean score of 41.0 with a standard
deviation of 3.7. Perform the hypothesis test at the 1% significance level.
25)
Two graphical displays are given for a set of data. A hypothesis test is to be performed for the mean of the population
from which the data were obtained. Would it be reasonable to use a one–mean z–test? Explain your reasoning. Assume
that the population standard deviation is known.
26)
A normal probability plot and a stem–and–leaf diagram of the data are given below.
26)
Provide an appropriate response.
27)
A hypothesis test for a population mean is to be performed. If the sample size is small (less
than 15), under what conditions is it reasonable to use the z–test? If the sample size is
moderate (between 15 and 30), under what conditions is it reasonable to use the z–test?
27)
28)
For a fixed sample size, how will increasing the significance level of a hypothesis test affect
the probability of a Type I error? How will it affect the probability of a Type II error?
28)
Construct a graph portraying the decision criterion for the specified hypothesis test.
29)
A hypothesis test for a population mean is conducted. The hypotheses are:
H0: µ=µ0
Ha: µµ0
The significance level is 0.01 and the critical values are –2.575 and 2.575. Sketch a normal
curve displaying the decision criterion. This curve will represent the normal curve for the
test statistic under the assumption that the null hypothesis is true. On your graph indicate
the area in each tail, the critical values, the rejection region, and the nonrejection region.
29)
17
30)
A hypothesis test for a population mean is conducted. The hypotheses are:
H0: µ=µ0
Ha: µ<µ0
The significance level is 0.08 and the critical value is –1.41. Sketch a normal curve
displaying the decision criterion. This curve will represent the normal curve for the test
statistic under the assumption that the null hypothesis is true. On your graph indicate the
area in the tail, the critical value, the rejection region, and the nonrejection region.
30)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
31)
Use a significance level of = 0.05 to test whether µ differs from12.3. The sample data
consist of 20 scores for which x=10.1 and s =2.2. State the null and alternative
hypotheses, compute the value of the test statistic, and find the P–value. State your
conclusion.
31)
Decide whether it appears reasonable to use a t–test to perform a hypothesis test for the mean in question. Explain your
answer and include any relevant graphs, such as a normal probability plot, histogram, or stem–and–leaf diagram. If there
are outliers, explain how to proceed.
32)
A machine that fills soda bottles is supposed to fill them to a mean volume of 16.2 fluid
ounces. A random sample of 20 filled bottles produced the following volumes in fluid
ounces: 16.3 15.9 16.7 15.3 17.1 16.4 3.9 15.9 16.2 3.4
16.4 8.2 15.5 16.5 16.0 16.3 15.8 16.7 16.5 15.5
32)
Perform a one–sample z–test for a population mean using the P–value approach. Be sure to state the hypotheses and the
significance level, to compute the value of the test statistic, to obtain the P–value, and to state your conclusion. Also,
assess the strength of the evidence against the null hypothesis.
33)
Five years ago, the average math SAT score for students at one school was 475. A teacher
wants to perform a hypothesis test to determine whether the mean math SAT score of
students at the school has changed. The mean math SAT score for a random sample of 40
students from this school is 469. Do the data provide sufficient evidence to conclude that
the mean math SAT score for students at the school has changed from the previous mean of
475? Perform the appropriate hypothesis test using a significance level of 10%. Assume
that = 73.
33)
Provide an appropriate response.
34)
A hypothesis test is performed at the 5% significance level to determine whether the mean
body temperature for a certain population differs from 37.1° C. The hypotheses are
H0: µ= 37.1° C
Ha: µ 37.1° C.
Explain the difference between statistical significance and practical significance.
34)
35)
A man is on trial accused of murder in the first degree. The prosecutor presents evidence
that he hopes will convince the jury to reject the hypothesis that the man is innocent. This
situation can be modeled as a hypothesis test with the following hypotheses:
H0: The defendant is innocent.
Ha: The defendant is guilty.
If convicted, the defendant will receive the death penalty. Do you think that a Type I error
or a Type II error would be more serious? Why?
35)
Perform a one–sample z–test for a population mean using the P–value approach. Be sure to state the hypotheses and the
significance level, to compute the value of the test statistic, to obtain the P–value, and to state your conclusion. Also,
assess the strength of the evidence against the null hypothesis.
36)
In 2000, the average duration of long–distance telephone calls originating in one town was
9.4 minutes. A long–distance telephone company wants to perform a hypothesis test to
determine whether the average duration of long–distance phone calls has changed from
the 2000 mean of 9.4 minutes. They randomly sampled 50 calls originating in the town and
found that the mean duration of these 50 calls was 8.6 minutes. Do the data provide
sufficient evidence to conclude that the mean call duration, µ, has changed from the 2000
mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of
1%. Assume that = 4.8 minutes.
36)
Provide an appropriate response.
37)
Suppose that you wish to perform a hypothesis test for a population mean. Under what
conditions would you choose to perform a t–test rather than a z–test? What conditions
must be satisfied for the t–test to work?
37)
38)
Outline the six steps involved in performing a one–sample z–test for a population mean.
38)
39)
A one–sample z–test for a population mean is to be performed. Why might it be more
useful for those interpreting the results to know the P–value rather than simply whether or
not the null hypothesis was rejected?
39)
40)
Suppose that you wish to perform a hypothesis test for a population mean using the
critical value method. The test is right–tailed. Suppose that the population standard
deviation is unknown. The correct procedure to use is the t–test. If you mistakenly use the
standard normal table to obtain the critical value, will the value that you obtain be larger
or smaller than the correct value? Does the mistaken use of the normal table make it more
or less likely that the null hypothesis will be rejected?
40)
Perform a one–sample z–test for a population mean using the P–value approach. Be sure to state the hypotheses and the
significance level, to compute the value of the test statistic, to obtain the P–value, and to state your conclusion. Also,
assess the strength of the evidence against the null hypothesis.
41)
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. For adult males, the mean FVC is 5.0 liters. A researcher wants to
perform a hypothesis test to determine whether the mean forced vital capacity for women
differs from this value. The mean forced vital capacity for a random sample of 85 women
was 4.8 liters. Do the data provide sufficient evidence to conclude that the mean forced
vital capacity for women differs from 5.0 liters, the mean value for men? Perform the
appropriate hypothesis test using a significance level of 5%. Assume that = 0.9 liters.
41)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
42)
In one state, the mean time served in prison by convicted burglars is 18.7 months. A
researcher would like to perform a hypothesis test to determine whether the mean amount
of time served by convicted burglars in her hometown is different from 18.7 months. She
takes a random sample of 11 such cases from court files in her home town and finds that
x=20.9 months and s =7.9 months. Use a 5% significance level to perform the test.
42)
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.
43)
A newspaper in a large midwestern city reported that the National Association of Realtors
said that the mean home price last year was $116,800. The city housing department feels
that this figure is too low. They randomly selected 63 home sales and obtained a sample
mean price of $118,900. Assume that the population standard deviation is $3,700. Using a
5% level of significance, perform a hypothesis test to determine whether the population
mean is higher than $116,800.
43)
Provide an appropriate response.
44)
A one–sample z–test for a population mean is to be performed. Compare the steps
involved in using the critical–value approach and the steps involved in using the P–value
approach. Which steps do the two methods have in common? How do the two methods
differ?
44)
45)
Give an example of a situation in which you might wish to conduct a right–tailed
hypothesis test concerning a population mean. State in words what you wish to determine
and write the null and alternative hypotheses in words and symbolically.
45)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
46)
Test whether the mean weight of female college students differs from 132 lb. The mean
weight for a random sample of 20 female college students was x= 137 lb with a standard
deviation, s, of 14.2 lb. Use a significance level of = 0.1.
46)
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.
47)
The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4
parts per million (ppm). A consumer health group measured the level of the chemical in a
random sample of tomatoes obtained from one producer. The levels, in ppm, are shown
below.
0.31 0.47 0.19 0.72 0.56
0.91 0.29 0.83 0.49 0.28
0.31 0.46 0.25 0.34 0.17
0.58 0.19 0.26 0.47 0.81
At the 5% significance level, do the data provide sufficient evidence to conclude that the
mean level of the chemical in tomatoes from this producer is greater than the
recommended level of 0.4 ppm? Assume that the population standard deviation of levels
of the chemical in these tomatoes is 0.21 ppm.
47)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
48)
Last year, the mean annual salary for adults in one town was $35,000. A researcher wants
to perform a hypothesis test to determine whether the mean annual salary for adults in this
town has changed. The mean annual salary for a random sample of 17 adults from the
town was x= $27,298 with a standard deviation, s, of $14,200. Use a significance level of
= 0.05.
48)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
49)
The mean waiting time for bus number 14 during peak hours used to be 10 minutes. A
public bus company official claims that more buses are now in service and that the mean
waiting time for bus number 14 during peak hours is now less than 10 minutes. Karen
took bus number 14 during peak hours on 18 different occasions. Her mean waiting time
was 7.2 minutes with a standard deviation of 1.9 minutes. At the 1% significance level, test
the claim that the mean is less than 10 minutes.
49)
Perform a one–sample z–test for a population mean using the P–value approach. Be sure to state the hypotheses and the
significance level, to compute the value of the test statistic, to obtain the P–value, and to state your conclusion. Also,
assess the strength of the evidence against the null hypothesis.
50)
A health insurer has determined that the “reasonable and customary” fee for a certain
medical procedure is $1200. They suspect that the average fee charged by one particular
clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis
test to determine whether their suspicion is correct. The mean fee charged by the clinic for
a random sample of 65 patients receiving this procedure was $1280. Do the data provide
sufficient evidence to conclude that the mean fee charged by this clinic for this procedure is
higher than $1200? Perform the appropriate hypothesis test using a significance level of
1%. Assume that = $220.
50)
Provide an appropriate response.
51)
A bottle filling machine fills 16–ounce bottles with juice. The amount of juice varies from
bottle to bottle, however the average amount of juice is supposed to be 16.0 ounces. The
manufacturer performs a hypothesis test to determine whether the machine is working
properly. The hypotheses are:
H0: µ= 16.0 ounces
Ha: µ< 16.0 ounces
Do you think that a consumer advocacy group would prefer to have a small probability
or a small probability? Why? Do you think that the manufacturer would prefer to have a
small probability or a small probability? Why?
51)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
52)
Use a 1% significance level to test the claim that µ> 2.85. The sample data consists of
9 scores for which x=3.27 and s =0.58.
52)
Provide an appropriate response.
53)
When performing a one–sample z–test for a population mean, what criterion do you use
for rejecting the null hypothesis using the critical value approach? using the P–value
approach? Assume that a right–tailed test is being performed.
53)
54)
A manufacturer claims that the mean weight of flour in its 32–ounce bags is 32.1 ounces. A
z–test is performed to determine whether the mean weight is actually less than this. The
hypotheses are
H0: µ= 32.1 ounces
Ha: µ< 32.1 ounces.
The mean weight for a sample of 45 bags of flour was 30.7 ounces. Suppose that the
P–value corresponding to this sample data is 0.001. Give an interpretation of the P–value.
Would you feel confident in concluding that the mean weight is less than 32.1 ounces?
54)
55)
Suppose that you wish to conduct a hypothesis test concerning a population mean. How
would you decide whether to conduct a right–tailed, a left–tailed, or a two–tailed test? Is it
acceptable to decide what type of test to conduct by examining the sample data?
55)
56)
Give an example of a hypothesis test for which it is important to have a small probability.
Explain why it is important to have a small value for .
56)
57)
Explain the difference between a Type I error and a Type II error.
57)
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.
58)
In tests of a computer component, it is found that the mean time between failures is
983 hours. A modification is made which is supposed to increase reliability by increasing
the time between failures. Tests on a sample of 36 modified components produce a mean
time between failures of 983 hours. Using a 1% level of significance, perform a hypothesis
test to determine whether the mean time between failures for the modified components is
greater than 937 hours. Assume that the population standard deviation is 52 hours.
58)
Construct a graph portraying the decision criterion for the specified hypothesis test.
59)
A hypothesis test for a population mean is conducted. The hypotheses are:
H0: µ=µ0
Ha: µ>µ0
The significance level is 0.01 and the critical value is 2.33. Sketch a normal curve
displaying the decision criterion. This curve will represent the normal curve for the test
statistic under the assumption that the null hypothesis is true. On your graph indicate the
area in the tail, the critical value, the rejection region, and the nonrejection region.
59)
29
Two graphical displays are given for a set of data. A hypothesis test is to be performed for the mean of the population
from which the data were obtained. Would it be reasonable to use a one–mean z–test? Explain your reasoning. Assume
that the population standard deviation is known.
60)
A normal probability plot and a stem–and–leaf diagram of the data are given below.
60)
Provide an appropriate response.
61)
A one–sample z–test for a population mean is to be performed. The hypotheses are
H0: µ= 100
Ha: µ 100.
Let z0 denote the observed value of the test statistic, z. Suppose that z0 is positive and
the P–value for the test is 0.07. Is the following a correct interpretation of the P–value? If
not, give a correct interpretation of the P–value. If the null hypothesis were true, the
probability of observing a value of the test statistic as large or larger than that observed
would be 0.07.
61)
Decide whether it appears reasonable to use a t–test to perform a hypothesis test for the mean in question. Explain your
answer and include any relevant graphs, such as a normal probability plot, histogram, or stem–and–leaf diagram. If there
are outliers, explain how to proceed.
31
62)
Test scores for a random sample of 12 students were as follows:
24 42 52 55 60 65
67 71 72 75 77 79
62)
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.
63)
A brochure claims that the average maximum height a certain type of plant is 0.7 m. A
gardener suspects that this estimate is not accurate locally due to soil conditions. A random
sample of 43 mature plants is taken. The mean height of the plants in the sample is 0.65 m.
Using a 1% level of significance, perform a hypothesis test to determine whether the
population mean is different from 0.7 m. Assume that the population standard deviation is
0.2 m.
63)
Construct a graph portraying the decision criterion for the specified hypothesis test.
64)
A hypothesis test for a population mean is conducted. The hypotheses are:
H0: µ=µ0
Ha: µ<µ0
The significance level is 0.10 and the critical value is –1.28. Sketch a normal curve
displaying the decision criterion. This curve will represent the normal curve for the test
statistic under the assumption that the null hypothesis is true. On your graph indicate the
area in the tail, the critical value, the rejection region, and the nonrejection region.
64)
33
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.
65)
In one city, convicted burglars are sentenced to an average of 18.7 months in prison. A
researcher wants to perform a hypothesis test to determine whether the mean sentence
handed down by one particular judge for burglars differs from 18.7 months. She takes a
random sample of 34 such cases from the court files of this judge and finds that x=16.6
months. Assume that the population standard deviation is 7.7 months. Test the hypothesis
at the 5% significance level.
65)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
66)
In tests of a computer component, it is found that the mean time between failures is
520 hours. A modification is made which is supposed to increase the time between failures.
Tests on a random sample of 10 modified components resulted in the following times (in
hours) between failures.
518 548 561 523 536
499 538 557 528 563
At the 5% significance level, test the claim that for the modified components, the mean
time between failures is greater than 520 hours.
66)
Provide an appropriate response.
67)
Jenny is conducting a hypothesis test concerning a population mean. The hypotheses are
as follows.
H0: µ= 50
Ha: µ> 50
She selects a sample and finds that the sample mean is 54.2. She then does some
calculations and is able to make the following statement:
If H0were true, the chance that the sample mean would have come out as big ( or bigger)
than 54.2 is 0.3. Do you think that she should reject the null hypothesis? Why or why not?
67)
68)
Suppose that you wish to perform a hypothesis test for a population mean. Suppose that
the population standard deviation is unknown, the population is normally distributed, and
the sample size is small. Would you perform a z–test or a t–test? Why? Would the test be
exact or approximate?
68)
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.
69)
The Maine Department of Natural Resources reported that the mean weight of lobsters
trapped in the state is 1.7 pounds. Carl Lewis is a lobster trapper off the coast of Maine.
Carl suspects that this figure is too high so he records the weights of a random sample of
43 lobsters that he trapped. The mean weight of the lobsters in the sample was
1.5 pounds. Using a 1% level of significance, perform a hypothesis test to determine
whether the population mean is lower than 1.7 pounds. Assume that the population
standard deviation is 0.6 pounds.
69)
Provide an appropriate response.
70)
You wish to test the hypotheses shown below.
H0: µ= 40
Ha: µ> 40
Would you be inclined to reject the null hypothesis if the sample mean turned out to be
much smaller than 40? Explain your thinking.
70)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
71)
A car manufacturer, Swanson, claims that the mean lifetime of one of its car engines is
greater than 220,000 miles, which is the mean lifetime of the engine of a competitor. The
mean lifetime for a random sample of 23 of the Swanson engines was x= 226,450 miles
with a standard deviation, s, of 11,500 miles. Test the Swanson’s claim using a significance
level of = 0.01.
71)
Provide an appropriate response.
72)
Suppose that you wish to perform a hypothesis test for a population mean. Suppose that
the population standard deviation is unknown, the population is skewed to the right, and
the sample is large. Would you perform a z–test or a t–test? Why? Would the test be exact
or approximate?
72)
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.
73)
A manufacturer makes steel bars that are supposed to have a mean length of 50 cm. A
retailer suspects that the bars are running too long. A sample of 43 bars is taken and their
mean length is determined to be 51 cm. Using a 1% level of significance, perform a
hypothesis test to determine whether the population mean is greater than 50 cm. Assume
that the population standard deviation is 3.6 cm.
73)
Decide whether it appears reasonable to use a t–test to perform a hypothesis test for the mean in question. Explain your
answer and include any relevant graphs, such as a normal probability plot, histogram, or stem–and–leaf diagram. If there
are outliers, explain how to proceed.
74)
The hourly salaries (in dollars) of 28 randomly selected working adults are as follows:
9 20 18 24 19 12 35
16 20 13 15 22 10 30
12 8 21 40 38 24 14
22 50 16 19 23 10 120
74)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the P–value approach.
75)
A light–bulb manufacturer advertises that the mean life for its light bulbs is 900 hours. A
random sample of 15 of its light bulbs resulted in the following lives in hours.
995 590 510 539 739 917 571 555
916 728 664 693 708 887 849
At the 10% significance level, do the data provide evidence that the mean life for the
company’s light bulbs differs from the advertised mean?
75)
Provide an appropriate response.
76)
Robert is conducting a hypothesis test concerning a population mean. The hypotheses are
as follows.
H0: µ= 50
Ha: µ> 50
He selects a sample of size 35 and finds that the sample mean is 60. He then does some
calculations and finds that for samples of size 35, the standard deviation of the sample
means is 3.2. Do you think that he should reject the null hypothesis? Why or why not?
76)
Perform a one–sample z–test for a population mean using the P–value approach. Be sure to state the hypotheses and the
significance level, to compute the value of the test statistic, to obtain the P–value, and to state your conclusion. Also,
assess the strength of the evidence against the null hypothesis.
77)
A car insurance company has determined that the mean annual car insurance cost for a
family in the town of Watlington is $1716. A researcher wants to perform a hypothesis test
to determine whether the mean insurance cost for a family in the town of Putford is higher
than this. The mean insurance cost for a random sample of 32 families in Putford was
$1761. At the 10% significance level, do the data provide sufficient evidence to conclude
that the mean insurance cost for a family in Putford is higher than $1716, the mean cost for
a family in Watlington.? Assume that the population standard deviation is $35.50.
77)
38
78)
A manufacturer claims that the mean amount of juice in its 16–ounce bottles is 16.1 ounces.
A consumer advocacy group wants to perform a hypothesis test to determine whether the
mean amount is actually less than this. The mean volume of juice for a random sample of
70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the
mean amount of juice for the 16–ounce bottles, µ, is less than 16.1 ounces? Perform the
appropriate hypothesis test using a significance level of 10%. Assume that = 0.9 ounces.
78)
Decide whether it appears reasonable to use a t–test to perform a hypothesis test for the mean in question. Explain your
answer and include any relevant graphs, such as a normal probability plot, histogram, or stem–and–leaf diagram. If there
are outliers, explain how to proceed.
79)
Lifetimes (in hours) for a random sample of 12 batteries are as follows:
57 59 61 64 72 76
80 86 93 95 100 102
79)
Two graphical displays are given for a set of data. A hypothesis test is to be performed for the mean of the population
from which the data were obtained. Would it be reasonable to use a one–mean z–test? Explain your reasoning. Assume
that the population standard deviation is known.
40
80)
A normal probability plot and a histogram plot of the data are given below.
80)
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.
81)
The National Weather Service says that the mean daily high temperature for October in a
large midwestern city is 56°F. A local weather service suspects that this value is not
accurate and wants to perform a hypothesis test to determine whether the mean is actually
lower than 56°F. A sample of mean daily high temperatures for October over the past 37
years yields x= 54°F. Assume that the population standard deviation is 5.6° F. Perform the
hypothesis test at the 1% significance level.
81)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
82)
A large software company gives job applicants a test of programming ability and the mean
for that test has been 160 in the past. Twenty–five job applicants are randomly selected
from a large university and they produce a mean score of 183 and standard deviation of 12.
Use a 5% significance level to test whether the mean score for students from this university
is greater than 160.
82)
Perform a one–sample z–test for a population mean using the P–value approach. Be sure to state the hypotheses and the
significance level, to compute the value of the test statistic, to obtain the P–value, and to state your conclusion. Also,
assess the strength of the evidence against the null hypothesis.
83)
Last year, the mean running time for a certain type of flashlight battery was 8.5 hours. This
year, the manufacturer has introduced a change in the production method which he hopes
will increase the mean running time. A random sample of 40 of the new light bulbs was
obtained and the mean running time was found to be 8.7 hours. Do the data provide
sufficient evidence to conclude that the mean running time, µ, of the new light bulbs is
larger than last year’s mean of 8.5 hours? Perform the appropriate hypothesis test using a
significance level of 5%. Assume that = 0.5 hours.
83)
84)
The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4
parts per million (ppm). A consumer health group measured the level of the chemical in a
random sample of tomatoes obtained from one producer. The levels, in ppm, are shown
below.
0.31 0.47 0.19 0.72 0.56
0.91 0.29 0.83 0.49 0.28
0.31 0.46 0.25 0.34 0.17
0.58 0.19 0.26 0.47 0.81
At the 5% significance level, do the data provide sufficient evidence to conclude that the
mean level of the chemical in tomatoes from this producer is greater than the
recommended level of 0.4 ppm? Assume that the population standard deviation of levels
of the chemical in these tomatoes is 0.21 ppm.
84)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
85)
Use a 5% significance level to test the claim that µ 32.6. The sample data consists of
15 scores for which x=39.3 and s =7.
85)
Provide an appropriate response.
86)
Give an example of a situation in which you might wish to conduct a two–tailed
hypothesis test concerning a population mean. State in words what you wish to determine
and write the null and alternative hypotheses in words and symbolically.
86)
Preliminary data analyses indicate that it is reasonable to use a t–test to carry out the specified hypothesis test. Perform
the t–test using the critical–value approach.
87)
A light–bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A
random sample of 15 of its light bulbs resulted in the following lives in hours.
995 590 510 539 739 917 571 555
916 728 664 693 708 887 849
At the 10% significance level, do the data provide evidence that the mean life for the
company’s light bulbs differs from the advertised mean?
87)
Provide an appropriate response.
88)
A right–tailed hypothesis test for a population mean is to be performed. If the null
hypothesis is rejected at the 5% level of significance, does this necessarily mean that it
would be rejected at the 1% level of significance? at the 10% level of significance? Explain
your reasoning. In your explanation, refer to the critical values corresponding to the
different significance levels.
88)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Classify the conclusion of the hypothesis test as a Type I error, a Type II error, or a correct decision.
89)
In 2000, the average duration of long–distance telephone calls originating in one town was
9.4 minutes. Five years later, in 2005, a long–distance telephone company performs a hypothesis
test to determine whether the average duration of long–distance phone calls has changed from the
2000 mean of 9.4 minutes. The hypotheses are:
H0: µ= 9.4 minutes
Ha: µ 9.4 minutes
where µ is the mean duration, in 2005, of long–distance telephone calls originating in the town.
Suppose that the results of the sampling lead to nonrejection of the null hypothesis. Classify that
conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean duration of
long–distance phone calls has changed from the 2000 mean of 9.4 minutes.
89)
A)
Type I error
B)
Type II error
C)
Correct decision
Determine the critical value(s) for a one–mean z–test.
90)
Find the critical value(s) for a two–tailed test with = 0.02 and draw a graph that illustrates your
answer.
90)
A)
–2.05, 2.05
B)
–2.05
C)
–1.75, 1.75
45
D)
–2.33, 2.33
A sample mean, sample standard deviation, and sample size are given. Use the one–mean t–test to perform the required
hypothesis test about the mean, µ, of the population from which the sample was drawn. Use the P–value approach. Also,
assess the strength of the evidence against the null hypothesis.
91)
x= 84.5, s = 11.2, n = 16, H0: µ= 80, Ha: µ< 80, = 0.01.
91)
A)
Test statistic: t = 1.61. P–value = 0.9356. Do not reject the null hypothesis. There is not
sufficient evidence to conclude that the mean is less than 80. The evidence against the null
hypothesis is weak or none.
B)
Test statistic: t = 1.61. P–value = 0.9463. Do not reject the null hypothesis. There is not
sufficient evidence to conclude that the mean is less than 80. The evidence against the null
hypothesis is weak or none.
C)
Test statistic: t = 1.61. P–value = 0.0644. Do not reject the null hypothesis. There is not
sufficient evidence to conclude that the mean is less than 80. The evidence against the null
hypothesis is moderate.
D)
Test statistic: t = 1.61. P–value = 0.9356. Reject the null hypothesis. There is sufficient
evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is
very strong.
The P–value for a hypothesis test is given. Determine whether the strength of the evidence against the null hypothesis is
weak/none, moderate, strong, or very strong.
92)
P = 0.034
92)
A)
Very strong
B)
Weak or none
C)
Strong
D)
Moderate
Classify the hypothesis test as two–tailed, left–tailed, or right–tailed.
93)
The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to
maintain a true mean temperature, µ, of 48°F, ideal for a certain type of German pilsner. The owner
of the brewery does not agree with the refrigerator manufacturer, and will conduct a hypothesis
test to determine whether the true mean temperature differs from this value.
93)
A)
Two–tailed
B)
Left–tailed
C)
Right–tailed
The value obtained for the test statistic, z, in a one–mean z–test is given. Also given is whether the test is two tailed, left
tailed, or right tailed. Determine the P–value.
94)
A left–tailed test:
z = –2.65
94)
A)
0.9960
B)
0.0040
C)
0.0080
D)
0.9920
Provide an appropriate response.
95)
A one–sample z–test for a population mean is performed. Suppose that the P–value for the test is
0.04. For what significance levels (values of ) can the null hypothesis be rejected?
95)
A)
For all values of smaller than 0.04
B)
For all values of greater than or equal to 0.04
C)
For = 0.04
D)
For = 0.05, 0.10
A sample mean, sample size, and population standard deviation are given. Use the one–mean z–test to perform the
required hypothesis test at the given significance level. Use the critical –value approach.
96)
x=51, n =45 , = 3.6, H0: µ= 50; Ha: µ> 50, = 0.01
96)
A)
z =1.86;critical value = 2.33; reject H0
B)
z =1.86;critical value = 1.33; reject H0
C)
z =1.86;critical value = 2.33; do not reject H0
D)
z = 0.28; critical value = 2.33; do not reject H0
For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.
97)
In the past, the mean running time for a certain type of flashlight battery has been 8.9 hours. The
manufacturer has introduced a change in the production method and wants to perform a
hypothesis test to determine whether the mean running time has increased as a result. The
hypotheses are:
H0: µ=8.9 hours
Ha: µ>8.9 hours
where µ is the mean running time of the new batteries . Explain the meaning of a Type II error.
97)
A)
A Type II error would occur if, in fact, µ>8.9 hours, but the results of the sampling lead to the
conclusion that µ<8.9 hours.
B)
A Type II error would occur if, in fact, µ>8.9 hours, but the results of the sampling fail to
lead to that conclusion.
C)
A Type II error would occur if, in fact, µ=8.9 hours, but the results of the sampling do not
lead to rejection of that fact.
D)
A Type II error would occur if, in fact, µ=8.9 hours, but the results of the sampling lead to the
conclusion that µ>8.9 hours.
A sample mean, sample size, and population standard deviation are given. Use the one–mean z–test to perform the
required hypothesis test at the given significance level. Use the critical –value approach.
98)
x=7.9, n = 18 , =1.7, H0: µ= 10; Ha: µ< 10, = 0.01
98)
A)
z= –5.24; critical value = –2.33; reject H0
B)
z= –5.24; critical value = 1.96; do not reject H0
C)
z= –5.24; critical value = –1.96; reject H0
D)
z= –5.24; critical value = –2.33; do not reject H0
A sample mean, sample size, and population standard deviation are given. Use the one–mean z–test to perform the
required hypothesis test at the given significance level. Use the P–value approach.
99)
x= 3.7, n = 32, = 1.8, H0: µ = 4.2 , Ha: µ < 4.2 , = 0.05
99)
A)
z = –1.57; P–value = 0.1164; do not reject H0
B)
z = –1.57; P–value = 0.0582; reject H0
C)
z = –1.57; P–value = 0.1164; reject H0
D)
z = –1.57; P–value = 0.0582; do not reject H0.
The significance level and P–value of a hypothesis test are given. Decide whether the null hypothesis should be rejected.
100)
= 0.05, P–value = 0.014
100)
A)
Reject the null hypothesis.
B)
Do not reject the null hypothesis.
The graph portrays the decision criterion for a one–mean z–test. The curve in the graph is the normal curve for the test
statistic under the assumption that the null hypothesis is true. Use the graph to solve the problem.
101)
A graphical display of the decision criterion follows.
Determine the rejection region.
101)
A)
–2.33
z
2.33
B)
z –2.33 or z
2.33
C)
z = –2.33 or z = 2.33
D)
z 0.01
A hypothesis test is to be performed. Determine the null and alternative hypotheses.
102)
A health insurer has determined that the “reasonable and customary” fee for a certain medical
procedure is $1200. They suspect that the average fee charged by one particular clinic for this
procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine
whether their suspicion is correct.
102)
A)
H0: µ= $1200
Ha: µ< $1200
B)
H0: µ> $1200
Ha: µ= $1200
C)
H0: µ= $1200
Ha: µ> $1200
D)
H0: µ= $1200
Ha: µ $1200
The significance level and P–value of a hypothesis test are given. Decide whether the null hypothesis should be rejected.
103)
= 0.10, P–value = 0.16
103)
A)
Reject the null hypothesis.
B)
Do not reject the null hypothesis.
A sample mean, sample standard deviation, and sample size are given. Use the one–mean t–test to perform the required
hypothesis test about the mean, µ, of the population from which the sample was drawn. Use the critical–value approach.
104)
x=3.12 , s =0.59, n = 9, H0: µ= 2.85, Ha: µ> 2.85, = 0.01
104)
A)
Test statistic: t =1.37. Critical value: t =2.33. Do not reject H0. There is not sufficient evidence
to support the claim that the mean is greater than 2.85.
B)
Test statistic: t =1.37. Critical value: t =2.821. Do not reject H0. There is not sufficient
evidence to support the claim that the mean is greater than 2.85.
C)
Test statistic: t =1.37. Critical value: t =2.896. Do not reject H0. There is not sufficient
evidence to support the claim that the mean is greater than 2.85.
D)
Test statistic: t =1.37. Critical value: t =2.896. Reject H0. There is sufficient evidence to
support the claim that the mean is greater than 2.85.
Provide an appropriate response.
105)
The P–value for a one–mean t–test is estimated using a t–table as 0.05 < P < 0.10. Based on this
information, for what significance levels can the null hypothesis be rejected?
105)
A)
We can reject H0 at any significance level smaller than 0.10.
B)
We can reject H0 at any significance level 0.10 or larger.
C)
We can reject H0 at any significance level smaller than 0.05.
D)
We can reject H0 at any significance level 0.05 or larger.
Use a table of t–values to estimate the P–value for the specified one–mean t–test.
106)
Left–tailed test, n = 15, t = –2.677
106)
A)
P > 0.005
B)
0.01 < P < 0.025
C)
P < 0.005
D)
0.005 < P < 0.01
Provide an appropriate response.
107)
A one–sample z–test for a population mean is to be performed. Let z0 denote the observed value
of the test statistic, z. Assume that a two–tailed test is being performed. True or false: If z0 is
negative, the P–value is twice the area under the standard normal curve to the right of z0.
107)
A)
True
B)
False
The graph portrays the decision criterion for a one–mean z–test. The curve in the graph is the normal curve for the test
statistic under the assumption that the null hypothesis is true. Use the graph to solve the problem.
108)
A graphical display of the decision criterion follows.
Determine the critical value(s).
108)
A)
z –1.96
B)
= 0.025
C)
z = –1.96
D)
z = ±1.96
A hypothesis test is to be performed. Determine the null and alternative hypotheses.
109)
In the past, the mean running time for a certain type of flashlight battery has been 8.1 hours. The
manufacturer has introduced a change in the production method and wants to perform a
hypothesis test to determine whether the mean running time has changed as a result.
109)
A)
H0: µ8.1 hours
Ha: µ=8.1 hours
B)
H0: µ=8.1 hours
Ha: µ8.1 hours
C)
H0: µ=8.1 hours
Ha: µ>8.1 hours
D)
H0: µ8.1 hours
Ha: µ=8.1 hours
A sample mean, sample standard deviation, and sample size are given. Use the one–mean t–test to perform the required
hypothesis test about the mean, µ, of the population from which the sample was drawn. Use the critical–value approach.
110)
x= 137, s = 14.2, n = 20, H0: µ= 132, Ha: µ
132, = 0.1
110)
A)
Test statistic: t = 1.57. Critical values: t = ±1.645. Do not reject H0. There is not sufficient
evidence to conclude that the mean is different from 132.
B)
Test statistic: t = 0.35. Critical values: t = ±1.729. Do not reject H0. There is not sufficient
evidence to conclude that the mean is different from 132.
C)
Test statistic: t = 0.35. Critical values: t = ±1.645. Do not reject H0. There is not sufficient
evidence to conclude that the mean is different from 132.
D)
Test statistic: t = 1.57. Critical values: t = ±1.729. Do not reject H0. There is not sufficient
evidence to conclude that the mean is different from 132.
Classify the hypothesis test as two–tailed, left–tailed, or right–tailed.
111)
The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. A
hypothesis test is to be performed to decide whether adult women are, on average, getting less than
the RDA of 75 milligrams per day.
111)
A)
Two–tailed
B)
Left–tailed
C)
Right–tailed
For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.
112)
In the past, the mean running time for a certain type of flashlight battery has been 8.2 hours. The
manufacturer has introduced a change in the production method and wants to perform a
hypothesis test to determine whether the mean running time has increased as a result. The
hypotheses are:
H0: µ=8.2 hours
Ha: µ>8.2 hours
where µ is the mean running time of the new batteries . Explain the meaning of a Type I error.
112)
A)
A Type I error would occur if, in fact, µ=8.2 hours, but the results of the sampling lead to the
conclusion that µ>8.2 hours.
B)
A Type I error would occur if, in fact, µ=8.2 hours, but the results of the sampling do not lead
to rejection of that fact.
C)
A Type I error would occur if, in fact, µ>8.2 hours, but the results of the sampling fail to lead
to that conclusion.
D)
A Type I error would occur if, in fact, µ>8.2 hours, but the results of the sampling lead to the
conclusion that µ<8.2 hours.
The P–value for a hypothesis test is given. Determine whether the strength of the evidence against the null hypothesis is
weak/none, moderate, strong, or very strong.
113)
P = 0.096
113)
A)
Strong
B)
Weak or none
C)
Moderate
D)
Very strong
114)
P = 0.054
114)
A)
Weak or none
B)
Very strong
C)
Strong
D)
Moderate
115)
P = 0.71
115)
A)
Strong
B)
Moderate
C)
Weak or none
D)
Very strong
Classify the hypothesis test as two–tailed, left–tailed, or right–tailed.
116)
At one school, the average amount of time that tenth–graders spend watching television each week
is 21.6 hours. The principal introduces a campaign to encourage the students to watch less
television. One year later, the principal wants to perform a hypothesis test to determine whether
the average amount of time spent watching television per week has decreased from the previous
mean of 21.6 hours.
116)
A)
Two–tailed
B)
Left–tailed
C)
Right–tailed
The P–value for a hypothesis test is given. Determine whether the strength of the evidence against the null hypothesis is
weak/none, moderate, strong, or very strong.
117)
P = 0.0097
117)
A)
Weak or none
B)
Moderate
C)
Very strong
D)
Strong
Explanation:
Use a table of t–values to estimate the P–value for the specified one–mean t–test.
118)
Right–tailed test, n = 19, t = 2.418
118)
A)
0.025 < P < 0.05
B)
P > 0.10
C)
0.05 < P < 0.10
D)
0.01 < P < 0.025
Explanation:
Explanation:
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