Chapter 9
62. What is the p-value for this hypothesis test, rounded to four decimal places?
63. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 64-67:
A researcher wants to test if the elementary school children spend less than 30 minutes per day
on homework. A random sample of 64 children from the school shows that they spend an
average of 24.5 minutes per day on homework. Assume that
=
15.3 minutes, and that the test
is to be made at the 1% significance level.
64. What is the critical value of z?
A) -2.06 B) -2.33 C) -2.58 D) -1.96
65. What is the value of the test statistic, z, rounded to three decimal places?
66. What is the p-value for this hypothesis test, rounded to four decimal places?
67. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Chapter 9
68. We use the t distribution to perform a hypothesis test about the population mean when:
A) the population from which the sample is drawn is approximately normal and the
population standard deviation is known
B) the population from which the sample is drawn is not approximately normal and
the population standard deviation is known
C) the population from which the sample is drawn is approximately normal and the
population standard deviation is unknown
D) the population from which the sample is drawn is not approximately normal and
the population standard deviation is unknown
69. Which of the following conditions is not required to use the t distribution to perform a
hypothesis test about a population mean?
A) The population from which the sample is drawn is approximately normal
B) The population from which the sample is drawn has a t distribution
C) The population standard deviation is unknown
D) The sample does not have any extreme outliers
Use the following to answer questions 70-73:
In a hypothesis test with hypotheses
0: 54H
and
1: 54H
, a random sample of 24
elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4.
The test is to be made at the 10% significance level. Assume the population is normally
distributed.
70. What is the critical value of t?
A) 1.318 B) 1.28 C) -1.319 D) 1.319
71. What is the value of the test statistic, t, rounded to three decimal places?
72. What is the p-value for this hypothesis test, rounded to four decimal places?
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73. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 74-77:
In a hypothesis test with hypotheses
0: 90H
=
and
1: 90H
, a random sample of 16
elements selected from the population produced a mean of 91.9 and a standard deviation of 4.9.
The test is to be made at the 2% significance level. Assume the population is normally
distributed.
74. What are the critical values of t?
A) -2.33 and 2.33 C) -2.131 and 2.131
B) -2.602 and 2.602 D) -2.583 and 2.583
75. What is the value of the test statistic, t, rounded to three decimal places?
76. What is the p-value for this hypothesis test, rounded to four decimal places?
77. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 78-81:
In a hypothesis test with hypotheses
0: 74H
and
1: 74H
, a random sample of 20
elements selected from the population produced a mean of 67.8 and a standard deviation of 11.9.
The significance level is 5%. Assume the population is normally distributed.
Chapter 9
78. What is the critical value of t?
A) -1.645 B) -1.725 C) -1.729 D) -2.093
79. What is the value of the test statistic, t, rounded to three decimal places?
80. What is the p-value for this hypothesis test, rounded to four decimal places?
81. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 82-86:
A company that manufactures light bulbs claims that its light bulbs last an average of 1,150
hours. A sample of 25 light bulbs manufactured by this company gave a mean life of 1,097 hours
and a standard deviation of 133 hours. A consumer group wants to test the hypothesis that the
mean life of light bulbs produced by this company is less than 1,150 hours. The significance
level is 5%. Assume the population is normally distributed.
82. What is the critical value of t?
A) -1.704 B) -1.711 C) -2.797 D) -2.787
83. What is the value of the test statistic, t, rounded to three decimal places?
84. What is the p-value for this hypothesis test, rounded to four decimal places?
Chapter 9
85. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
86. Does the data provide evidence to contradict the company’s claim about the average
lifetime of their light bulbs? (State your answer as “no” or “yes”, but don’t include the
quotation marks.)
Use the following to answer questions 87-90:
In a hypothesis test with hypotheses
0: .39Hp
and
1: .39Hp
, a random sample of size 481
produced a sample proportion of 0.4350. The test is to be made at the 5% significance level.
87. What is the critical value of z?
A) 1.96 B) 1.645 C) 2.12 D) 2.72
88. What is the value of the test statistic, z, rounded to three decimal places?
89. What is the p-value for this hypothesis test, rounded to four decimal places?
90. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Chapter 9
Use the following to answer questions 91-94:
In a hypothesis test with hypotheses
0: 0.76Hp
and
1: 0.76Hp
, a random sample of size
974 produced a sample proportion of 0.7380. The test is to be made at the 5% significance level.
91. What is the critical value of z?
A) -2.05 B) -2.33 C) -1.96 D) -1.65
92. What is the value of the test statistic, z, rounded to three decimal places?
93. What is the p-value for this hypothesis test, rounded to four decimal places?
94. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 95-98:
In a hypothesis test with hypotheses
0: 0.26Hp=
and
1: 0.26Hp
, a random sample of size
809 produced a sample proportion of 0.2400. The test is to be made at the 5% significance level.
95. What are the critical values of z?
A) -2.58 and 2.58 C) -1.96 and 1.96
B) -1.645 and 1.645 D) -1.72 and 1.72
96. What is the value of the test statistic, z, rounded to three decimal places?
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97. What is the p-value for this hypothesis test, rounded to four decimal places?
98. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 99-102:
In a hypothesis test with hypotheses
0: 0.58Hp
and
1: 0.58Hp
, a random sample of size
1,165 produced a sample proportion of 0.6160. The test is to be made at the 2.5% significance
level.
99. What is the critical value of z?
A) 1.65 B) 2.33 C) 1.96 D) 2.58
100. What is the value of the test statistic, z, rounded to three decimal places?
101. What is the p-value for this hypothesis test, rounded to four decimal places?
102. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 103-106:
In a hypothesis test with hypotheses
0: 0.31Hp
and
1: 0.31Hp
, a random sample of size
530 produced a sample proportion of 0.2755. The test is to be made at the 2% significance level.
Chapter 9
103. What is the critical value of z?
A) -2.33 B) -2.05 C) -1.645 D) -1.714
104. What is the value of the test statistic, z, rounded to three decimal places?
105. What is the p-value for this hypothesis test, rounded to four decimal places?
106. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
107. Which of the following statements describes a Type II error in hypothesis testing?
A) A court declares a defendant guilty, when he is actually innocent.
B) A scientist, trying to support a theory about the number of different species of
animals in a particular country, declares the null hypothesis to be “there are 715
different species” when there are actually more than 800.
C) A statistician determines, through hypothesis testing, that the mean number of
televisions per household in a certain community is 1.4, when it is actually greater
than 1.4.
D) Through hypothesis testing, we find the alternative hypothesis to be true when it is
actually false.
108. The power of a hypothesis test is .96. Which of the following statements is true about this
test?
A) The probability of a Type II error is .04.
B) The probability of a Type I error is .04.
C) The probability of a Type II error is .96.
D) The probability of a Type I error is .96.
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109. A study conducted in 2000 found that the mean number of children under 18 per
household in a certain community was 1.7. A statistician is trying to determine whether
this number has changed in the last 6 years. Which of the following sets of hypotheses is
correct for this test?
A)
01
: 1.7; : 1.7HH
C)
01
: 1.7; : 1.7HH
=
B)
01
: 1.7; : 1.7HH
D)
01
: 1.7; : 1.7HH
Use the following to answer questions 110-113:
The director of a radio broadcast company wants to determine whether the mean length of
commercials on his station is equal to 24 seconds. A sample of 41 commercials had a mean life
of 26.90 seconds and a standard deviation of 7.88 seconds. The significance level is 5%.
110. What are the critical values of t?
A) -1.714 and 1.714 C) -2.010 and 2.010
B) -1.684 and 1.684 D) -2.021 and 2.021
111. What is the value of the test statistic, t, rounded to three decimal places?
112. What is the p-value for this hypothesis test, rounded to four decimal places?
113. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
Use the following to answer questions 114-118:
Thousands of people nationwide are to take part in a Spring Clean-Up day along highways near
their hometowns. The goal is to have individuals collect an average of 50 pounds (or more) of
garbage. In a random sample of 36 people, an average of 46.3 pounds was collected, with a
standard deviation of 9.2 pounds. The significance level is 2%.
Chapter 9
114. What is the critical value of t?
A) -1.803 B) -1.988 C) -2.133 D) -2.438
115. What is the value of the test statistic, t, rounded to three decimal places?
116. What is the p-value for this hypothesis test, rounded to four decimal places?
117. Should you reject or fail to reject the null hypothesis in this test? (State your answer as
“reject” or “fail to reject”, but don’t include the quotation marks.)
118. Does the data provide evidence to suggest that the goal is not being met? (State your
answer as “no” or “yes”, but don’t include the quotation marks.)
119. If the significance level of a hypothesis test is 5% we will reject the null hypothesis is the
p-value is
A) greater than 0.95 C) less than 0.05
B) less than 0.025 D) greater than 0.025
120. When
is unknown and the sample size is larger than 76, use:
A) a t test. B) a test for proportions. C) a z test. D) cannot perform a test.