Chapter 10
Use the following to answer questions 59-65:
A sample of 16 from a population produced a mean of 30.9 and a standard deviation of 4. A
sample of 18 from another population produced a mean of 33.1 and a standard deviation of 3.
Assume that the two populations are normally distributed and the standard deviations of the two
populations are not equal.
The null hypothesis is that the two population means are equal, while the alternative hypothesis
is that the mean of the first population is less than the mean of the second population. The
significance level is 1%.
59. What is the number of degrees of freedom of the t distribution to make a confidence
interval for the difference between the two population means?
60. What is the standard deviation of the sampling distribution of the difference between the
means of these two samples, rounded to three decimal places?
61. Derive the corresponding 95% confidence interval for the difference between the means
of these two populations, rounded to three decimal places.
62. What is the critical value of t for the hypothesis test?
A) -2.473 B) -2.080 C) -2.211 D) -2.425
63. What is the value of the test statistic, t, rounded to three decimal places?
64. What is the p-value for this test, rounded to four decimal places?
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65. Do you reject or fail to reject the null hypothesis? State your answer as “reject” or “fail to
reject”, but don’t include the quotation marks.
66. Two paired or matched samples would imply that:
A) data are collected on one variable from the elements of two independent samples
B) two data values are collected from the same source (elements) for two dependent
samples
C) two data values are collected from the same source (elements) for two independent
samples
D) data are collected on two variables from the elements of two independent samples
67. For two paired samples with sample size of n, the degrees of freedom are:
A) 2n – 1 B) 2n – 2 C) n – 1 D) n – 2
Use the following to answer questions 68-75:
Five persons, who were suffering from depression, attended 10 one-hour counseling sessions.
The following table gives the depression scores (on a scale of 1 to 10) of these five persons
before and after attending the counseling sessions. Note that a higher score means that a person
has a worse case of depression.
Before
After
7.5
4.3
6.4
5.1
7.1
6.2
9.7
6.9
7.8
7.2
Let the paired difference be the score before minus the score after attending the counseling
sessions. The null hypothesis is that the mean of the population paired differences is equal to
zero (i.e., attending the counseling sessions does not change the depression score). The
alternative hypothesis is that the mean of the population paired differences is not equal to zero
(i.e., attending the counseling sessions does change the depression score). The significance level
is 5%.
Chapter 10
68. What is the mean of the sample paired differences, rounded to two decimal places?
69. What is the standard deviation of the paired differences, rounded to three decimal places?
70. What is the standard deviation of the mean of the sample paired differences, rounded to
three decimal places?
71. Calculate the 95% confidence interval for the mean of the population paired differences
that corresponds to these data, rounded to two decimal places.
72. What are the critical values of t for the hypothesis test?
A) -2.776 and 2.776 C) -2.132 and 2.132
B) -2.571 and 2.571 D) -2.015 and 2.015
73. What is the value of the test statistic, t, rounded to three decimal places?
74. What is the p-value for this test, rounded to four decimal places?
75. Do you reject or fail to reject the null hypothesis? State your answer as “reject” or “fail to
reject”, but don’t include the quotation marks.
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Use the following to answer questions 76-83:
A city recently launched a neighborhood watch program to control crime. The following table
gives the number of crimes reported in six neighborhoods during the six months before and six
months after the city launched the neighborhood watch program.
Before
After
57
41
73
65
53
28
73
73
79
61
39
32
Let the paired difference be the number of crimes before minus the number of crimes after the
city launched the neighborhood watch program. The null hypothesis is that the mean of the
population paired differences is equal to zero (i.e., the neighborhood watch program does not
affect the number of crimes). The alternative hypothesis is that the mean of the population paired
differences is greater than zero (i.e., the neighborhood watch program decreases the number of
crimes). The significance level is 1%.
76. What is the mean of the sample paired differences, rounded to two decimal places?
77. What is the standard deviation of the paired differences, rounded to three decimal places?
78. What is the standard deviation of the mean of the sample paired differences, rounded to
three decimal places?
79. Calculate the 99% confidence interval for the mean of the population paired differences
that corresponds to these data, rounded to two decimal places.
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80. What are the critical values of t for the hypothesis test?
A) 3.143 B) 3.365 C) 3.747 D) 4.032
81. What is the value of the test statistic, t, rounded to three decimal places?
82. What is the p-value for this test, rounded to four decimal places?
83. Do you reject or fail to reject the null hypothesis? State your answer as “reject” or “fail
to reject”, but don’t include the quotation marks.
Use the following to answer questions 84-85:
The proportion of elements in a population that possess a certain characteristic is 0.66. The
proportion of elements in another population that possess the same characteristic is 0.77. You
select samples of 189 and 356 elements, respectively, from the first and second populations.
84. What is the mean of the sampling distribution of the difference between the two sample
proportions, rounded to two decimal places?
85. What is the standard deviation of the sampling distribution of the difference between the
two sample proportions, rounded to four decimal places?
Use the following to answer questions 86-87:
The proportion of elements in a population that possess a certain characteristic is 0.44. The
proportion of elements in another population that possess the same characteristic is 0.46. You
select samples of 988 and 867 elements, respectively, from the first and second populations.
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86. What is the mean of the sampling distribution of the difference between the two sample
proportions, reported to two decimal places?
87. What is the standard deviation of the sampling distribution of the difference between the
two sample proportions, rounded to four decimal places?
Use the following to answer questions 88-93:
A sample of 482 school teachers, who are married, showed that 209 of them hold a second job to
supplement their incomes. Another sample of 408 school teachers, who are single, showed that
135 of them hold a second job to supplement their incomes. The null hypothesis is that the
proportions of married and single school teachers who hold a second job to supplement their
incomes are not different. The alternative hypothesis is that the proportions of married and single
school teachers who hold a second job to supplement their incomes are different. The
significance level is 5%.
88. What is the 95% confidence interval for the difference between the proportions of
married and single school teachers who hold a second job to supplement their income,
rounded to four decimal places?
89. What are the critical values of z for the hypothesis test?
A) -2.33 and 2.33 B) -1.65 and 1.65 C) -2.17 and 2.17 D) -1.96 and 1.96
90. What is the value of the pooled sample proportion, rounded to four decimal places?
91. What is the value of the test statistic, z, rounded to three decimal places?
Chapter 10
92. What is the p-value for this test, rounded to four decimal places?
93. Do you reject or fail to reject the null hypothesis? State your answer as “reject” or “fail to
reject”, but don’t include the quotation marks.
Use the following to answer questions 94-99:
According to a Louis Harris survey, 500 in a sample of 983 female drivers reported that they
never speed, while 538 in a sample of 1218 male drivers report that they never speed. The null
hypothesis is that the proportions of all female and male drivers who never speed are the same.
The alternative hypothesis is that the proportion of female drivers who never speed is higher than
the proportion of male drivers who never speed. The significance level is 1%.
94. What is the 99% confidence interval for the difference between the proportions of female
and male drivers who state that they never speed, rounded to four decimal places?
95. What is the critical value of z for the hypothesis test?
A) 2.33 B) 2.05 C) 2.17 D) 2.58
96. What is the value of the pooled sample proportion, rounded to four decimal places?
97. What is the value of the test statistic, z, rounded to three decimal places?
98. What is the p-value for this test, rounded to four decimal places?
Chapter 10
99. Do you reject or fail to reject the null hypothesis? State your answer as “reject” or “fail to
reject”, but don’t include the quotation marks.
Use the following to answer questions 100-105:
In a survey regarding job satisfaction, 574 in a sample of 934 female job-holders stated that they
are satisfied with their jobs, while 500 in a sample of 755 male job-holders stated that they are
satisfied with their jobs. The null hypothesis is that the proportions of all female and male
job-holders who are satisfied with their jobs are the same. The alternative hypothesis is that the
proportion of female job-holders who are satisfied with their jobs is lower than the proportion of
male job-holders stated who are satisfied with their jobs. The significance level is 2.5%.
100. What is the 97% confidence interval for the difference between the proportions of all
female and all male job-holders who will say that they are satisfied with their job,
rounded to four decimal places?
101. What is the critical value of z for the hypothesis test?
A) -1.96 B) -2.17 C) -2.33 D) -2.05
102. What is the value of the pooled sample proportion, rounded to four decimal places?
103. What is the value of the test statistic, z, rounded to three decimal places?
104. What is the p-value for this test, rounded to four decimal places?
Chapter 10
105. Do you reject or fail to reject the null hypothesis? State your answer as “reject” or “fail to
reject”, but don’t include the quotation marks.
106. Calculate the observed value from these two samples. Round your answer to the nearest
tenth.
Sample from population 1: 2 2 3 4 2 2 8
Sample from population 2: 8 4 2 3 8 1
107. Suppose the following information comes from random samples from normal populations
with means and , respectively.
n1 = 13
30x=
s1 = 3.3
n2 = 17
29y=
s2 = 3
Using the data given, obtain a 95% confidence interval for the difference in means.
Round your answer to three decimal places.
Chapter 10
108. Consider the following statistics associated with a productivity index.
Group 1
2.514x=
10.773s=
Group 2
219n=
2.963y=
20.525s=
Do these data strongly indicate that the mean index for group 1 is lower than that for
group 2? Test at level
0.05
=
. Answer “Reject null hypothesis” or “Not reject null
hypothesis”.