Fundamentals of Hypothesis Testing: One-Sample Tests 9-1
CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS
TESTING: ONE-SAMPLE TESTS
1. Which of the following would be an appropriate null hypothesis?
a) The mean of a population is equal to 55.
b) The mean of a sample is equal to 55.
c) The mean of a population is greater than 55.
d) Only (a) and (c) are appropriate.
2. Which of the following would be an appropriate null hypothesis?
a) The population proportion is less than 0.65.
b) The sample proportion is less than 0.65.
c) The population proportion is not less than 0.65.
d) The sample proportion is no less than 0.65.
3. Which of the following would be an appropriate alternative hypothesis?
a) The mean of a population is equal to 55.
b) The mean of a sample is equal to 55.
c) The mean of a population is greater than 55.
d) The mean of a sample is greater than 55.
4. Which of the following would be an appropriate alternative hypothesis?
a) The population proportion is less than 0.65.
b) The sample proportion is less than 0.65.
c) The population proportion is not less than 0.65.
d) The sample proportion is not less than 0.65.
9-2 Fundamentals of Hypothesis Testing: One-Sample Tests
5. A Type II error is committed when
a) you reject a null hypothesis that is true.
b) you don’t reject a null hypothesis that is true.
c) you reject a null hypothesis that is false.
d) you don’t reject a null hypothesis that is false.
6. A Type I error is committed when
a) you reject a null hypothesis that is true.
b) you don’t reject a null hypothesis that is true.
c) you reject a null hypothesis that is false.
d) you don’t reject a null hypothesis that is false.
7. The power of a test is measured by its capability of
a) rejecting a null hypothesis that is true.
b) not rejecting a null hypothesis that is true.
c) rejecting a null hypothesis that is false.
d) not rejecting a null hypothesis that is false.
8. If an economist wishes to determine whether there is evidence that mean family income in a
community exceeds $50,000
a) either a one-tail or two-tail test could be used with equivalent results.
b) a one-tail test should be utilized.
c) a two-tail test should be utilized.
d) None of the above.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-3
9. If an economist wishes to determine whether there is evidence that mean family income in a
community equals $50,000
a) either a one-tail or two-tail test could be used with equivalent results.
b) a one-tail test should be utilized.
c) a two-tail test should be utilized.
d) None of the above.
10. If the p-value is less than
α
in a two-tail test,
a) the null hypothesis should not be rejected.
b) the null hypothesis should be rejected.
c) a one-tail test should be used.
d) no conclusion should be reached.
11. If a test of hypothesis has a Type I error probability (
α
) of 0.01, it means that
a) if the null hypothesis is true, you don’t reject it 1% of the time.
b) if the null hypothesis is true, you reject it 1% of the time.
c) if the null hypothesis is false, you don’t reject it 1% of the time.
d) if the null hypothesis is false, you reject it 1% of the time.
12. If the Type I error (
α
) for a given test is to be decreased, then for a fixed sample size n
a) the Type II error (
β
) will also decrease.
b) the Type II error (
β
) will increase.
c) the power of the test will increase.
d) a one-tail test must be utilized.
9-4 Fundamentals of Hypothesis Testing: One-Sample Tests
13. True or False: For a given level of significance, if the sample size is increased but the summary
statistics remain the same, the probability of committing a Type I error will increase.
14. True or False: For a given level of significance, if the sample size is increased but the summary
statistics remain the same, the probability of committing a Type II error will increase.
15. True or False: For a given sample size, the probability of committing a Type II error will increase
when the probability of committing a Type I error is reduced.
16. For a given sample size n, if the level of significance (
α
) is decreased, the power of the test
a) will increase.
b) will decrease.
c) will remain the same.
d) cannot be determined.
17. For a given level of significance (
α
), if the sample size n is increased, the probability of a Type
II error (
β
)
a) will decrease.
b) will increase.
c) will remain the same.
d) cannot be determined.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-5
18. You know that the level of significance (
α
) of a test is 5%, you can tell that the probability of
committing a Type II error (
β
) is
a) 2.5%
b) 95%.
c) 97.5%
d) unknown
19. You know that the probability of committing a Type II error (
β
) is 5%, you can tell that the
power of the test is
a) 2.5%
b) 95%.
c) 97.5%
d) unknown
20. If a researcher rejects a true null hypothesis, she has made a _______error.
21. If a researcher does not reject a true null hypothesis, she has made a _______decision.
22. If a researcher rejects a false null hypothesis, she has made a _______decision.
9-6 Fundamentals of Hypothesis Testing: One-Sample Tests
23. If a researcher does not reject a false null hypothesis, she has made a _______error.
24. It is possible to directly compare the results of a confidence interval estimate to the results
obtained by testing a null hypothesis if
a) a two-tail test for
μ
is used.
b) a one-tail test for
μ
is used.
c) Both of the previous statements are true.
d) None of the previous statements is true.
25. The power of a statistical test is
a) the probability of not rejecting H0 when it is false.
b) the probability of rejecting H0 when it is true.
c) the probability of not rejecting H0 when it is true.
d) the probability of rejecting H0 when it is false.
26. The symbol for the power of a statistical test is
a)
α
.
b) 1 –
α
.
c)
β
.
d) 1 –
β
.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-7
27. The symbol for the probability of committing a Type I error of a statistical test is
a)
α
.
b) 1 –
α
.
c)
β
.
d) 1 –
β
.
28. The symbol for the level of significance of a statistical test is
a)
α
.
b) 1 –
α
.
c)
β
.
d) 1 –
β
.
29. The symbol for the probability of committing a Type II error of a statistical test is
a)
α
.
b) 1 –
α
.
c)
β
.
d) 1 –
β
.
30. The symbol for the confidence coefficient of a statistical test is
a)
α
.
b) 1 –
α
.
c)
β
.
d) 1 –
β
.
9-8 Fundamentals of Hypothesis Testing: One-Sample Tests
31. Suppose we wish to test H0:
μ
≤ 47 versus H1:
μ
> 47. What will result if we conclude that the
mean is greater than 47 when its true value is really 52?
a) We have made a Type I error.
b) We have made a Type II error.
c) We have made a correct decision
d) None of the above are correct.
32. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?
Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose
a random sample of 100 Kleenex users yielded the following data on the number of tissues used
during a cold:
X
= 52, S = 22. Give the null and alternative hypotheses to determine if the
number of tissues used during a cold is less than 60.
a)
H
0:
μ
≤60 and
H
1:
μ
>60.
b)
H
0:
μ
≥60 and
H
1:
μ
<60.
c) H0: X ≥60 and H1: X <60.
d) H0: X =52 and H1: X ≠52.
33. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?
Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose
a random sample of 100 Kleenex users yielded the following data on the number of tissues used
during a cold:
X
= 52, S = 22. Using the sample information provided, calculate the value of the
test statistic.
a)
()
52 60 / 22t=−
b)
()( )
52 60 / 22 /100t=−
c)
()
()
2
52 60 / 22 /100t=−
d)
()()
52 60 / 22 /10t=−
Fundamentals of Hypothesis Testing: One-Sample Tests 9-9
34. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?
Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose
a random sample of 100 Kleenex users yielded the following data on the number of tissues used
during a cold:
X
= 52, S = 22. Suppose the alternative you wanted to test was
H
1:
μ
<60 . State
the correct rejection region for
α
= 0.05.
a) Reject H0 if t > 1.6604.
b) Reject H0 if t < – 1.6604.
c) Reject H0 if t > 1.9842 or Z < – 1.9842.
d) Reject H0 if t < – 1.9842.
35. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?
Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose
a random sample of 100 Kleenex users yielded the following data on the number of tissues used
during a cold:
X
= 52, S = 22. Suppose the test statistic does fall in the rejection region at
α
=
0.05. Which of the following decision is correct?
a) At
α
= 0.05, you do not reject H0.
b) At
α
= 0.05, you reject H0.
c) At
α
= 0.05, you do not reject H0.
d) At
α
= 0.10, you do not reject H0.
36. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?
Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose
a random sample of 100 Kleenex users yielded the following data on the number of tissues used
during a cold:
X
= 52, S = 22. Suppose the test statistic does fall in the rejection region at
α
=
0.05. Which of the following conclusion is correct?
a) At
α
= 0.05, there is not sufficient evidence to conclude that the mean number of tissues
used during a cold is 60 tissues.
b) At
α
= 0.05, there is sufficient evidence to conclude that the mean number of tissues
used during a cold is 60 tissues.
c) At
α
= 0.05, there is insufficient evidence to conclude that the mean number of tissues
used during a cold is not 60 tissues.
d) At
α
= 0.10, there is sufficient evidence to conclude that the mean number of tissues
used during a cold is not 60 tissues.
9-10 Fundamentals of Hypothesis Testing: One-Sample Tests
37. You have created a 95% confidence interval for
μ
with the result 10 15
μ
≤≤ . What decision
will you make if you test
H
0:
μ
=16 versus
H
1:
μ
≠16 at
α
= 0.05?
a) Reject H0 in favor of H1.
b) Do not reject H0 in favor of H1.
c) Fail to reject H0 in favor of H1.
d) We cannot tell what our decision will be from the information given.
38. You have created a 95% confidence interval for
μ
with the result 10 15
μ
≤≤ . What decision
will you make if we test
H
0:
μ
=16 versus
H
1:
μ
≠16 at
α
= 0.10?
a) Reject H0 in favor of H1.
b) Do not reject H0 in favor of H1.
c) Fail to reject H0 in favor of H1.
d) We cannot tell what our decision will be from the information given.
16.
KEYWORDS: mean, t test, two-tail test, confidence interval, decision
39. You have created a 95% confidence interval for
μ
with the result 10 15
μ
≤≤ . What decision
will you make if we test
H
0:
μ
=16 versus
H
1:
μ
≠16 at
α
= 0.01?
a) Reject H0 in favor of H1.
b) Do not reject H0 in favor of H1.
c) Fail to reject H0 in favor of H1.
d) You cannot tell what our decision will be from the information given.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-11
40. Suppose you want to test
H
0:
μ
≥30 versus
H
1:
μ
<30. Which of the following possible
sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of
H1?
a)
X
= 28, S = 6
b)
X
= 27, S = 4
c)
X
= 32, S = 2
d)
X
= 26, S = 9
41. Which of the following statements is not true about the level of significance in a hypothesis test?
a) The larger the level of significance, the more likely you are to reject the null hypothesis.
b) The level of significance is the maximum risk we are willing to accept in making a Type I
error.
c) The significance level is also called the
α
level.
d) The significance level is another name for Type II error.
42. If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have
committed
a) a Type II error.
b) a Type I error.
c) no error.
d) an acceptance error.
43. The value that separates a rejection region from a non-rejection region is called the _______.
9-12 Fundamentals of Hypothesis Testing: One-Sample Tests
44. A is a numerical quantity computed from the data of a sample and is used
in reaching a decision on whether or not to reject the null hypothesis.
a) significance level
b) critical value
c) test statistic
d) parameter
45. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of
the club. She would now like to determine whether or not the mean age of her customers is
greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no
entertainment changes will be made. The appropriate hypotheses to test are:
a)
H
0:
μ
≥30 versus
H
1:
μ
<30.
b)
H
0:
μ
≤30 versus
H
1:
μ
>30.
c) H0:X ≥30 versus H1:X <30 .
d) H0:X ≤30 versus H1:X >30 .
46. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of
the club. She would now like to determine whether or not the mean age of her customers is
greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no
entertainment changes will be made. If she wants to have a level of significance at 0.01, what
rejection region should she use?
a) Reject H0 if t < – 2.3263.
b) Reject H0 if t < – 2.5758.
c) Reject H0 if t > 2.3263.
d) Reject H0 if t > 2.5758.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-13
47. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of
the club. She would now like to determine whether or not the mean age of her customers is
greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no
entertainment changes will be made. Suppose she found that the sample mean was 30.45 years
and the sample standard deviation was 5 years. If she wants to have a level of significance at
0.01, what decision should she make?
a) Reject H0.
b) Reject H1.
c) Do not reject H0.
d) We cannot tell what her decision should be from the information given.
48. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of
the club. She would now like to determine whether or not the mean age of her customers is
greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no
entertainment changes will be made. Suppose she found that the sample mean was 30.45 years
and the sample standard deviation was 5 years. If she wants to have a level of significance at 0.01
what conclusion can she make?
a) There is not sufficient evidence that the mean age of her customers is greater than 30.
b) There is sufficient evidence that the mean age of her customers is greater than 30.
c) There is not sufficient evidence that the mean age of her customers is not greater than 30.
d) There is sufficient evidence that the mean age of her customers is not greater than 30.
49. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of
the club. She would now like to determine whether or not the mean age of her customers is
greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no
entertainment changes will be made. Suppose she found that the sample mean was 30.45 years
and the sample standard deviation was 5 years. What is the p-value associated with the test
statistic?
a) 0.3577
b) 0.1423
c) 0.0780
d) 0.02
9-14 Fundamentals of Hypothesis Testing: One-Sample Tests
50. An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims
that over the past 5 years, the mean daily revenue was $675 with a population standard deviation
of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null
hypothesis that the daily mean revenue was $675, which test would you use?
a) Z-test of a population mean
b) Z-test of a population proportion
c) t-test of population mean
d) t-test of a population proportion
51. An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims
that over the past 5 years, the mean daily revenue was $675 with a population standard deviation
of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null
hypothesis that the daily mean revenue was $675 and decide not to reject the null hypothesis,
what can you conclude?
a) There is not enough evidence to conclude that the daily mean revenue was $675.
b) There is not enough evidence to conclude that the daily mean revenue was not $675.
c) There is enough evidence to conclude that the daily mean revenue was $675.
d) There is enough evidence to conclude that the daily mean revenue was not $675.
52. A manager of the credit department for an oil company would like to determine whether the mean
monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100
accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If
you were to conduct a test to determine whether the auditor should conclude that there is
evidence that the mean balance is different from $75, which test would you use?
a) Z-test of a population mean
b) Z-test of a population proportion
c) t-test of population mean
d) t-test of a population proportion
Fundamentals of Hypothesis Testing: One-Sample Tests 9-15
53. A manager of the credit department for an oil company would like to determine whether the mean
monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100
accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If
you wanted to test whether the mean balance is different from $75 and decided to reject the null
hypothesis, what conclusion could you reach?
a) There is not evidence that the mean balance is $75.
b) There is not evidence that the mean balance is not $75.
c) There is evidence that the mean balance is $75.
d) There is evidence that the mean balance is not $75.
54. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To
test this claim against the alternative that the actual proportion of doctors who recommend aspirin
is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend
aspirin. The value of the test statistic in this problem is approximately equal to:
a) – 4.12
b) – 2.33
c) – 1.86
d) – 0.07
55. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To
test this claim against the alternative that the actual proportion of doctors who recommend aspirin
is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is –
2.20. Can you conclude that H0 should be rejected at the (a)
α
= 0.10, (b)
α
= 0.05, and (c)
α
=
0.01 level of Type I error?
a) (a) yes; (b) yes; (c) yes
b) (a) no; (b) no; (c) no
c) (a) no; (b) no; (c) yes
d) (a) yes; (b) yes; (c) no
9-16 Fundamentals of Hypothesis Testing: One-Sample Tests
56. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To
test this claim against the alternative that the actual proportion of doctors who recommend aspirin
is less than 0.90, a random sample of 100 doctors was selected. Suppose you reject the null
hypothesis. What conclusion can you reach?
a) There is not sufficient evidence that the proportion of doctors who recommend aspirin is
not less than 0.90.
b) There is sufficient evidence that the proportion of doctors who recommend aspirin is not
less than 0.90.
c) There is not sufficient evidence that the proportion of doctors who recommend aspirin is
less than 0.90.
d) There is sufficient evidence that the proportion of doctors who recommend aspirin is less
than 0.90.
57. A pizza chain is considering opening a new store in an area that currently does not have any such
stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in
the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected
households in the area and finds that 96 have a favorable view. State the test of hypothesis that is
of interest to the pizza chain.
a) 32.0: versus 32.0: 10 >≤
π
π
HH
b) 25.0: versus 25.0: 10 >≤
π
π
HH
c) 000,5: versus 000,5: 10 >≤
π
π
HH
d)
H
0:
μ
≤5,000 versus
H
1:
μ
>5,000
58. A pizza chain is considering opening a new store in an area that currently does not have any such
stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in
the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected
households in the area and finds that 96 have a favorable view. The value of the test statistic in
this problem is approximately equal to:
a) 2.80
b) 2.60
c) 1.94
d) 1.30
Fundamentals of Hypothesis Testing: One-Sample Tests 9-17
59. A pizza chain is considering opening a new store in an area that currently does not have any such
stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in
the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected
households in the area and finds that 96 have a favorable view. The p-value associated with the
test statistic in this problem is approximately equal to:
a) 0.0100
b) 0.0051
c) 0.0026
d) 0.0013
60. A pizza chain is considering opening a new store in an area that currently does not have any such
stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in
the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected
households in the area and finds that 96 have a favorable view. The decision on the hypothesis
test using a 5% level of significance is:
a) to reject H0 in favor of H1.
b) to accept H0 in favor of H1.
c) to fail to reject H0 in favor of H1.
d) we cannot tell what the decision should be from the information given.
61. A pizza chain is considering opening a new store in an area that currently does not have any such
stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in
the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected
households in the area and finds that 96 have a favorable view. The pizza chain’s conclusion from
the hypothesis test using a 5% level of significance is:
a) to open a new store.
b) not to open a new store.
c) to delay opening a new store until additional evidence is collected.
d) we cannot tell what the decision should be from the information given.
9-18 Fundamentals of Hypothesis Testing: One-Sample Tests
62. The marketing manager for an automobile manufacturer is interested in determining the proportion of
new compact-car owners who would have purchased a GPS navigation system if it had been available
for an additional cost of $300. The manager believes from previous information that the proportion is
0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they
would have purchased the GPS navigation system. If you were to conduct a test to determine whether
there is evidence that the proportion is different from 0.30, which test would you use?
a) Z-test of a population mean
b) Z-test of a population proportion
c) t-test of population mean
d) t-test of a population proportion
63. The marketing manager for an automobile manufacturer is interested in determining the
proportion of new compact-car owners who would have purchased a GPS navigation system if it
had been available for an additional cost of $300. The manager believes from previous
information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is
selected and 79 indicate that they would have purchased the GPS navigation system. If you were
to conduct a test to determine whether there is evidence that the proportion is different from 0.30
and decided not to reject the null hypothesis, what conclusion could you reach?
a) There is sufficient evidence that the proportion is 0.30.
b) There is not sufficient evidence that the proportion is 0.30.
c) There is sufficient evidence that the proportion is 0.30.
d) There is not sufficient evidence that the proportion is not 0.30.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-19
SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift. She
will make her decision using a test with a level of significance of 0.10. The following information
was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: 0:20H
μ
≤; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
64. Referring to Scenario 9-1, the parameter the manager is interested in is:
a) the mean number of defective light bulbs per case produced at the plant.
b) the mean number of defective light bulbs per case among the 46 cases.
c) the mean number of defective light bulbs per case produced during the morning shift.
d) the proportion of cases with defective light bulbs produced at the plant.
65. Referring to Scenario 9-1, state the alternative hypothesis for this study.
μ
66. Referring to Scenario 9-1, what critical value should the manager use to determine the rejection
region?
a) 1.6794
b) 1.3011
c) 1.3006
d) 0.6800
67. True or False: Referring to Scenario 9-1, the null hypothesis would be rejected.
9-20 Fundamentals of Hypothesis Testing: One-Sample Tests
68. True or False: Referring to Scenario 9-1, the null hypothesis would be rejected if a 5% probability
of committing a Type I error is allowed.
69. True or False: Referring to Scenario 9-1, the null hypothesis would be rejected if a 1% probability
of committing a Type I error is allowed.
70. Referring to Scenario 9-1, the lowest level of significance at which the null hypothesis can be
rejected is ______.
71. True or False: Referring to Scenario 9-1, the evidence proves beyond a doubt that the mean
number of defective bulbs per case is greater than 20 during the morning shift.
72. True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient
evidence to show that the mean number of defective bulbs per case is greater than 20 during the
morning shift using a level of significance of 0.10.
73. True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient
evidence to show that the mean number of defective bulbs per case is greater than 20 during the
morning shift with no more than a 5% probability of incorrectly rejecting the true null hypothesis.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-21
74. True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient
evidence to show that the mean number of defective bulbs per case is greater than 20 during the
morning shift with no more than a 1% probability of incorrectly rejecting the true null hypothesis.
75. True or False: Referring to Scenario 9-1, if these data were used to perform a two-tail test, the p-
value would be 0.042.
76. True or False: Suppose, in testing a hypothesis about a mean, the p-value is computed to be
0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.
77. True or False: Suppose, in testing a hypothesis about a mean, the p-value is computed to be
0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.
78. True or False: Suppose, in testing a hypothesis about a mean, the Z test statistic is computed to be
2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-
tail test is used.
79. True or False: In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.
9-22 Fundamentals of Hypothesis Testing: One-Sample Tests
80. True or False: The test statistic measures how close the computed sample statistic has come to the
hypothesized population parameter.
81. True or False: The statement of the null hypothesis always contains an equality.
82. True or False: The larger the p-value, the more likely you are to reject the null hypothesis.
83. True or False: The smaller the p-value, the stronger is the evidence against the null hypothesis.
84. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19. If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be rejected at a level of
significance of 0.05.
85. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19. If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the
mean of the population differs from 18, the null hypothesis could be rejected at a level of
significance of 0.05.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-23
86. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19. If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be rejected at a level of
significance of 0.10.
87. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19. If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be rejected at a level of
significance of 0.02.
88. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19. If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be accepted at a level of
significance of 0.01.
89. True or False: In testing a hypothesis, you should always raise the question concerning the
purpose of the study, survey or experiment.
90. True or False: A proper methodology in performing hypothesis tests is to ask whether a random
sample can be selected from the population of interest.
9-24 Fundamentals of Hypothesis Testing: One-Sample Tests
91. True or False: “What conclusions and interpretations can you reach from the results of the
hypothesis test?” is not an important question to ask when performing a hypothesis test.
92. True or False: “Is the intended sample size large enough to achieve the desired power of the test
for the level of significance chosen?” should be among the questions asked when performing a
hypothesis test
93. True or False: In instances in which there is insufficient evidence to reject the null hypothesis,
you must make it clear that this does not prove that the null hypothesis is true.
94. True or False: In instances in which there is insufficient evidence to reject the null hypothesis,
you must make it clear that this has proven that the null hypothesis is true.
95. True or False: In conducting research, you should document both good and bad results.
96. True or False: You should report only the results of hypothesis tests that show statistical
significance and omit those for which there is insufficient evidence in the findings.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-25
SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses. Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time. When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time. Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
97. Referring to Scenario 9-2, what would be a Type I error?
a) Saying that the person is a business major when in fact the person is a business major.
b) Saying that the person is a business major when in fact the person is an agriculture major.
c) Saying that the person is an agriculture major when in fact the person is a business major.
d) Saying that the person is an agriculture major when in fact the person is an agriculture
major.
98. Referring to Scenario 9-2, what would be a Type II error?
a) Saying that the person is a business major when in fact the person is a business major.
b) Saying that the person is a business major when in fact the person is an agriculture major.
c) Saying that the person is an agriculture major when in fact the person is a business major.
d) Saying that the person is an agriculture major when in fact the person is an agriculture
major.
99. Referring to Scenario 9-2, what is the “actual level of significance” of the test?
a) 0.13
b) 0.16
c) 0.84
d) 0.87
9-26 Fundamentals of Hypothesis Testing: One-Sample Tests
100. Referring to Scenario 9-2, what is the “actual confidence coefficient”?
a) 0.13
b) 0.16
c) 0.84
d) 0.87
101. Referring to Scenario 9-2, what is the value of
α
?
a) 0.13
b) 0.16
c) 0.84
d) 0.87
102. Referring to Scenario 9-2, what is the value of
β
?
a) 0.13
b) 0.16
c) 0.84
d) 0.87
103. Referring to Scenario 9-2, what is the power of the test?
a) 0.13
b) 0.16
c) 0.84
d) 0.87
Fundamentals of Hypothesis Testing: One-Sample Tests 9-27
SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W. From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer
group has decided to try to discover if the claim appears true. They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
104. Referring to Scenario 9-3, the population of interest is
a) the power consumption in the 20 microwave ovens.
b) the power consumption in all such microwave ovens.
c) the mean power consumption in the 20 microwave ovens.
d) the mean power consumption in all such microwave ovens.
105. Referring to Scenario 9-3, the parameter of interest is
a) the mean power consumption of the 20 microwave ovens.
b) the mean power consumption of all such microwave ovens.
c) 250
d) 257.3
106. Referring to Scenario 9-3, the appropriate hypotheses to determine if the manufacturer’s claim
appears reasonable are:
a) 250 : versus250 : 10 ≠=
μ
μ
HH
b) 250 : versus250 : 10 <≥
μ
μ
HH
c) 250 : versus250 : 10 >≤
μ
μ
HH
d) 3.257 : versus3.257 : 10 <≥
μ
μ
HH
107. Referring to Scenario 9-3, for a test with a level of significance of 0.05, the critical value would
be ________.
9-28 Fundamentals of Hypothesis Testing: One-Sample Tests
108. Referring to Table 9.3, the value of the test statistic is ________.
109. Referring to Scenario 9-3, the p-value of the test is ________.
110. True or False: Referring to Scenario 9-3, for this test to be valid, it is necessary that the power
consumption for microwave ovens has a normal distribution.
111. True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 5% level of
significance.
112. True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 1% level of
significance.
113. True or False: Referring to Scenario 9-3, the consumer group can conclude that there is enough
evidence that the manufacturer’s claim is not true when allowing for a 5% probability of
committing a Type I error.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-29
SCENARIO 9-4
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic
the drug company is currently producing has a normal distribution with an mean of 7.4 minutes with a
standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time
should be normally distributed with the same standard deviation, but the mean effective time may be
lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue
to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will
be done to help make the decision.
114. Referring to Scenario 9-4, the appropriate hypotheses are:
a) 4.7 : versus 4.7 : 10 ≠=
μ
μ
HH
b) 4.7 : versus 4.7 : 10 >≤
μ
μ
HH
c) 4.7 : versus 4.7 : 10 <≥
μ
μ
HH
d) 4.7 : versus 4.7 : 10 ≤>
μ
μ
HH
115. Referring to Scenario 9-4, for a test with a level of significance of 0.10, the critical value would
be ________.
116. Referring to Scenario 9-4, the value of the test statistic is ________.
117. Referring to Scenario 9-4, the p-value of the test is ________.
9-30 Fundamentals of Hypothesis Testing: One-Sample Tests
118. True or False: Referring to Scenario 9-4, the null hypothesis will be rejected with a level of
significance of 0.10.
119. True or False: Referring to Scenario 9-4, if the level of significance had been chosen as 0.05,
the null hypothesis would be rejected.
120. True or False: Referring to Scenario 9-4, if the level of significance had been chosen as 0.05,
the company would market the new anesthetic.
SCENARIO 9-5
A bank tests the null hypothesis that the mean age of the bank’s mortgage holders is less than or equal
to 45 years, versus an alternative that the mean age is greater than 45 years. They take a sample and
calculate a p-value of 0.0202.
121. True or False: Referring to Scenario 9-5, the null hypothesis would be rejected at a significance
level of
α
= 0.05.
122. True or False: Referring to Scenario 9-5, the null hypothesis would be rejected at a significance
level of
α
= 0.01.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-31
123. True or False: Referring to Scenario 9-5, the bank can conclude that the mean age is greater
than 45 at a significance level of
α
= 0.01.
124. Referring to Scenario 9-5, if the same sample was used to test the opposite one-tail test, what
would be that test’s p-value?
a) 0.0202
b) 0.0404
c) 0.9596
d) 0.9798
SCENARIO 9-6
The quality control engineer for a furniture manufacturer is interested in the mean amount of force
necessary to produce cracks in stressed oak furniture. She performs a two-tail test of the null
hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test
statistic is a positive number that leads to a p-value of 0.080 for the test.
125. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of
0.10, the null hypothesis would be rejected.
126. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of
0.10, the engineer can conclude that the mean amount of force necessary to produce cracks in
stressed oak furniture is 650.
9-32 Fundamentals of Hypothesis Testing: One-Sample Tests
127. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of
0.05, the null hypothesis would be rejected.
128. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of
0.05, the engineer can conclude that the mean amount of force necessary to produce cracks in
stressed oak furniture is 650.
129. True or False: Referring to Scenario 9-6, suppose the engineer had decided that the alternative
hypothesis to test was that the mean was greater than 650. Then if the test is performed with a
level of significance of 0.05, the null hypothesis would be rejected.
130. Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to
test was that the mean was greater than 650. What would be the p-value of this one-tail test?
a) 0.040
b) 0.160
c) 0.840
d) 0.960
Fundamentals of Hypothesis Testing: One-Sample Tests 9-33
131. Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to
test was that the mean was less than 650. What would be the p-value of this one-tail test?
a) 0.040
b) 0.160
c) 0.840
d) 0.960
132. True or False: Referring to Scenario 9-6, suppose the engineer had decided that the alternative
hypothesis to test was that the mean was less than 650. Then if the test is performed with a level
of significance of 0.05, the null hypothesis would be rejected.
SCENARIO 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company’s
history. A series of new television advertisements featuring well-known entertainers and sports
figures were launched. A key metric for the success of television advertisements is the proportion of
viewers who “like the ads a lot”. A study of 1,189 adults who viewed the ads reported that 230
indicated that they “like the ads a lot.” The percentage of a typical television advertisement receiving
the “like the ads a lot” score is believed to be 22%. Company officials wanted to know if there is
evidence that the series of television advertisements are less successful than the typical ad (i.e. if there
is evidence that the population proportion of “like the ads a lot” for the company’s ads is less than
0.22) at a 0.01 level of significance.
133. Referring to Scenario 9-7, the parameter the company officials is interested in is:
a) the mean number of viewers who “like the ads a lot”.
b) the total number of viewers who “like the ads a lot”.
c) the mean number of company officials who “like the ads a lot”.
d) the proportion of viewers who “like the ads a lot”.
134. Referring to Scenario 9-7, state the null hypothesis for this study.
9-34 Fundamentals of Hypothesis Testing: One-Sample Tests
135. Referring to Scenario 9-7, state the alternative hypothesis for this study.
136. Referring to Scenario 9-7, what critical value should the company officials use to determine the
rejection region?
137. Referring to Scenario 9-7, the null hypothesis will be rejected if the test statistic is
a) greater than 2.3263
b) less than 2.3263
c) greater than −2.3263
d) less than −2.3263
138. True or False: Referring to Scenario 9-7, the null hypothesis would be rejected.
139. Referring to Scenario 9-7, the lowest level of significance at which the null hypothesis can be
rejected is ______.
140. Referring to Scenario 9-7, the largest level of significance at which the null hypothesis will not
be rejected is ______.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-35
141. True or False: Referring to Scenario 9-7, the company officials can conclude that there is
sufficient evidence to show that the series of television advertisements are less successful than the
typical ad using a level of significance of 0.01.
142. True or False: Referring to Scenario 9-7, the company officials can conclude that there is
sufficient evidence to show that the series of television advertisements are less successful than the
typical ad using a level of significance of 0.05.
143. True or False: Referring to Scenario 9-7, the value of
β
is 0.90.
144. Referring to Scenario 9-7, what will be the p-value if these data were used to perform a two-tail
test?
9-36 Fundamentals of Hypothesis Testing: One-Sample Tests
SCENARIO 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is
measured by the conversion rate, the percentage of browsers who buy something in their visit to a
site. The conversion rate for a company’s website was 10.1%. The website at the company was
redesigned in an attempt to increase its conversion rates. A sample of 200 browsers at the redesigned
site was selected. Suppose that 24 browsers made a purchase. The company officials would like to
know if there is evidence of an increase in conversion rate at the 5% level of significance.
145. Referring to Scenario 9-8, the parameter the company officials is interested in is:
a) the mean number of browsers who buy something in their visit to the company’s website.
b) the total number of browsers who buy something in their visit to the company’s website.
c) the mean number of company officials who buy something in their visit to the company’s
website.
d) the proportion of browsers who buy something in their visit to the company’s website.
146. Referring to Scenario 9-8, state the null hypothesis for this study.
147. Referring to Scenario 9-8, state the alternative hypothesis for this study.
148. Referring to Scenario 9-8, what critical value should the company officials use to determine the
rejection region?
Fundamentals of Hypothesis Testing: One-Sample Tests 9-37
149. Referring to Scenario 9-8, the null hypothesis will be rejected if the test statistic is
a) greater than 1.645
b) less than 1.645
c) greater than −1.645
d) less than −1.645
150. True or False: Referring to Scenario 9-8, the null hypothesis would be rejected.
151. Referring to Scenario 9-8, the lowest level of significance at which the null hypothesis can be
rejected is ______.
152. Referring to Scenario 9-8, the largest level of significance at which the null hypothesis will not
be rejected is ______.
KEYWORDS: one-tail test, proportion, Z test, p-value
153. True or False: Referring to Scenario 9-8, the company officials can conclude that there is
sufficient evidence that the conversion rate at the company’s website has increased using a level
of significance of 0.05.
154. True or False: Referring to Scenario 9-8, the value of the probability of committing a Type II
error
β
is 0.95.
9-38 Fundamentals of Hypothesis Testing: One-Sample Tests
155. Referring to Scenario 9-8, what will be the p-value if these data were used to perform a two-tail
test?
SCENARIO 9-9
The president of a university claimed that the entering class this year appeared to be larger than the
entering class from previous years but their mean SAT score is lower than previous years. He took a
sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a
standard deviation of 53. The university’s record indicates that the mean SAT score for entering
students from previous years is 1,520. He wants to find out if his claim is supported by the evidence
at a 5% level of significance.
156. Referring to Scenario 9-9, the parameter the president is interested in is:
a) the mean number of entering students to his university this year.
b) the mean number of entering students to all U.S. universities this year.
c) the mean SAT score of the entering students to his university this year.
d) the mean SAT score of the entering students to all U.S. universities this year.
157. Referring to Scenario 9-9, the population the president is interested in is:
a) all entering students to all universities in the U.S this year.
b) all entering students to his university this year.
c) all SAT test centers in the U.S. this year.
d) the SAT scores of all students entering universities in the U.S. this year .
158. Referring to Scenario 9-9, state the null hypothesis for this study.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-39
159. Referring to Scenario 9-9, state the alternative hypothesis for this study.
160. Referring to Scenario 9-9, what critical value should the president use to determine the
rejection region?
161. True or False: Referring to Scenario 9-9, the null hypothesis would be rejected.
162. True or False: Referring to Scenario 9-9, the null hypothesis would be rejected if a 10%
probability of committing a Type I error is allowed.
163. True or False: Referring to Scenario 9-9, the null hypothesis would be rejected if a 1%
probability of committing a Type I error is allowed.
164. Referring to Scenario 9-9, the lowest level of significance at which the null hypothesis can still
be rejected is ______.
9-40 Fundamentals of Hypothesis Testing: One-Sample Tests
165. Referring to Scenario 9-9, the highest level of significance at which the null hypothesis cannot
be rejected is ______.
166. True or False: Referring to Scenario 9-9, the evidence proves beyond a doubt that the mean
SAT score of the entering class this year is lower than previous years.
167. True or False: Referring to Scenario 9-9, the president can conclude that the mean SAT score of
the entering class this year is lower than previous years using a level of significance of 0.10.
168. True or False: Referring to Scenario 9-9, the president can conclude that there is sufficient
evidence to show that the mean SAT score of the entering class this year is lower than previous
years with no more than a 5% probability of incorrectly rejecting the true null hypothesis.
169. True or False: Referring to Scenario 9-9, the president can conclude that there is sufficient
evidence to show that the mean SAT score of the entering class this year is lower than previous
years with no more than a 10% probability of incorrectly rejecting the true null hypothesis.
170. True or False: Referring to Scenario 9-9, if these data were used to perform a two-tail test, the
p-value would be 0.1254.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-41
171. Referring to Scenario 9-9, which of the following best describes the Type I error?
a) The president concludes that the mean SAT score of the entering students is lower than
previous years when it is indeed not lower.
b) The president concludes that the mean SAT score of the entering students is higher than
previous years when it is indeed not higher.
c) The president concludes that the mean SAT score of the entering students is not lower
than previous years when it is indeed lower.
d) The president concludes that the mean SAT score of the entering students is not higher
than previous years when it is indeed higher.
172. Referring to Scenario 9-9, which of the following best describes the Type II error?
a) The president concludes that the mean SAT score of the entering students is lower than
previous years when it is indeed not lower.
b) The president concludes that the mean SAT score of the entering students is higher than
previous years when it is indeed not higher.
c) The president concludes that the mean SAT score of the entering students is not lower
than previous years when it is indeed lower.
d) The president concludes that the mean SAT score of the entering students is not higher
than previous years when it is indeed higher.
SCENARIO 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production
process is working properly. Based on past experience, the population standard deviation is 50 hours
and the light bulb life is normally distributed. The operations manager stops the production process if
there is evidence that the population mean light bulb life is below 500 hours.
173. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.10, the probability of a Type II error is _____ if the population mean
bulb life is 490 hours.
9-42 Fundamentals of Hypothesis Testing: One-Sample Tests
174. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.10, the probability of a Type I error is _____ if the population mean
bulb life is 510 hours.
175. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.10, the confidence coefficient of the test is _____ if the population mean
bulb life is 510 hours.
176. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.05, the probability of the operations manager failing to stop the process
when the process is not working properly is _____ if the population mean bulb life is 490 hours.
177. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.05, the probability of the operations manager incorrectly stopping the
process when the process is in fact working properly is _____.
178. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.05, the probability of the operations manager not stopping the process
when the process is in fact working properly is in fact below 500 hours is _____.
Fundamentals of Hypothesis Testing: One-Sample Tests 9-43
179. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.01, the probability of the operations manager failing to stop the process
if the population mean bulb life is 490 hours is _____.
180. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.01, the probability of the operations manager incorrectly stopping the
process if the population mean bulb life is 510 hours is _____.
181. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.01, the probability of the operations manager not stopping the process if
the population mean bulb life is 510 hours is _____.