Two-Sample Tests 10-1
CHAPTER 10: TWO-SAMPLE TESTS
1. True or False: For all two-sample tests, the sample sizes must be equal in the two groups.
2. True or False: When the sample sizes are equal, the pooled variance of the two groups is the
average of the 2 sample variances.
3. The t test for the difference between the means of 2 independent populations assumes that the
respective
a) sample sizes are equal.
b) sample variances are equal.
c) populations are approximately normal.
d) All of the above.
4. If we are testing for the difference between the means of 2 independent populations presuming
equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
a) 39.
b) 38.
c) 19.
d) 18.
10-2 Two-Sample Tests
5. In testing for the differences between the means of 2 independent populations where the variances
in each population are unknown but assumed equal, the degrees of freedom are
a) n – 1.
b) n1 + n2 – 1.
c) n1 + n2 – 2.
d) n – 2.
6. In testing for differences between the means of two independent populations, the null hypothesis
is:
a) 01 2
: H
μμ
− = 2.
b)
H
0:
μ
1–
μ
2 = 0.
c)
H
0:
μ
1–
μ
2 > 0.
d)
H
0:
μ
1–
μ
2 < 2.
7. In testing for the differences between the means of two independent populations, you assume that
the 2 populations each follow a _______ distribution.
8. Given the following information, calculate the degrees of freedom that should be used in the
pooled-variance t test.
s12 = 4 s22 = 6
n1 = 16 n2 = 25
a) df = 41
b) df = 39
c) df = 16
d) df = 25
Two-Sample Tests 10-3
9. Given the following information, calculate sp2, the pooled sample variance that should be used in
the pooled-variance t test.
s12 = 4 s22 = 6
n1 = 16 n2 = 25
a) sp2 = 6.00
b) sp2 = 5.00
c) sp2 = 5.23
d) sp2 = 4.00
10. True or False: The sample size in each independent sample must be the same if we are to test for
differences between the means of two independent populations.
11. True or False: When you test for differences between the means of two independent populations,
you can only use a two-tail test.
12. True or False: A statistics professor wanted to test whether the grades on a statistics test were the
same for upper and lower classmen. The professor took a random sample of size 10 from each,
conducted a test and found out that the variances were equal. For this situation, the professor
should use a t test with related samples.
13. True or False: A statistics professor wanted to test whether the grades on a statistics test were the
same for upper and lower classmen. The professor took a random sample of size 10 from each,
conducted a test and found out that the variances were equal. For this situation, the professor
should use a t test with independent samples.
10-4 Two-Sample Tests
SCENARIO 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each
were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation
for upward mobility. The SSATL scores are summarized below.
American Japanese
Sample Size 211 100
Sample Mean SSATL Score 65.75 79.83
Sample Std. Dev. 11.07 6.41
14. Referring to Scenario 10-1, judging from the way the data were collected, which test would likely
be most appropriate to employ?
a) Paired t test
b) Pooled-variance t test for the difference between two means
c) F test for the ratio of two variances
d) Z test for the difference between two proportions
15. Referring to Scenario 10-1, give the null and alternative hypotheses to determine if the mean
SSATL score of Japanese managers differs from the mean SSATL score of American managers.
a)
H
0:
μ
A–
μ
J≥0 versus
H
1:
μ
A–
μ
J<0
b)
H
0:
μ
A–
μ
J≤0 versus
H
1:
μ
A–
μ
J>0
c)
H
0:
μ
A–
μ
J=0 versus
H
1:
μ
A–
μ
J≠0
d) H0: X
A–X
J=0 versus H1: X
A–X
J≠0
16. Referring to Scenario 10-1, what is the value of the test statistic?
a) -14.08
b) -11.8092
c) -1.9677
d) 96.4471
Two-Sample Tests 10-5
17. Referring to Scenario 10-1, find the p-value if we assume that the alternative hypothesis was a
two-tail test.
a) Smaller than 0.01
b) Between 0.01 and 0.05
c) Between 0.05 and 0.10
d) Greater than 0.10
SCENARIO 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their
starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The
result of the pooled-variance t-test of the mean salaries of the females (Population 1) and males
(Population 2) in the sample is given below.
Hypothesized Difference 0
Level of Significance 0.05
Population 1 Sample
Sample Size 18
Sample Mean 99210
Sample Standard Deviation 13577
Population 2 Sample
Sample Size 12
Sample Mean 105820
Sample Standard Deviation 11741
Difference in Sample Means -6610
t Test Statistic -1.37631
Lower-Tail Test
Lower Critical Value -1.70113
p-Value 0.089816
18. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female
MBA graduates have a significantly lower mean starting salary than the male MBA graduates.
Which of the following is an appropriate alternative hypothesis?
a) 1 females males
:H
μμ
>
b) 1 females males
:H
μμ
<
c) 1 females males
:H
μμ
≠
d) 1 females males
:H
μμ
=
10-6 Two-Sample Tests
19. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female
MBA graduates have a significantly lower mean starting salary than the male MBA graduates.
From the analysis in Scenario 10-2, the correct test statistic is:
a) -6610
b) -1.3763
c) -1.7011
d) 0.0898
20. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female
MBA graduates have a significantly lower mean starting salary than the male MBA graduates.
The proper conclusion for this test is:
a) At the
α
= 0.10 level, there is sufficient evidence to indicate a difference in the mean
starting salaries of male and female MBA graduates.
b) At the
α
= 0.10 level, there is sufficient evidence to indicate that females have a lower
mean starting salary than male MBA graduates.
c) At the
α
= 0.10 level, there is sufficient evidence to indicate that females have a higher
mean starting salary than male MBA graduates.
d) At the
α
= 0.10 level, there is insufficient evidence to indicate any difference in the
mean starting salaries of male and female MBA graduates.
21. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female
MBA graduates have a significantly lower mean starting salary than the male MBA graduates.
What assumptions were necessary to conduct this hypothesis test?
a) Both populations of salaries (male and female) must have approximate normal
distributions.
b) The population variances are approximately equal.
c) The samples were randomly and independently selected.
d) All of the above assumptions were necessary.
Two-Sample Tests 10-7
22. Referring to Scenario 10-2, what is the 99% confidence interval estimate for the difference
between two means?
23. Referring to Scenario 10-2, what is the 95% confidence interval estimate for the difference
between two means?
24. Referring to Scenario 10-2, what is the 90% confidence interval estimate for the difference
between two means?
SCENARIO 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have
been living in their current homes is less than families in Metropolis. Assume that the two population
variances are equal.A random sample of 100 families from Gotham and a random sample of 150
families in Metropolis yield the following data on length of residence in current homes.
Gotham:
X
G = 35 months, SG2 = 900 Metropolis:
X
M = 50 months, SM2 = 1050
25. Referring to Scenario 10-3, which of the following represents the relevant hypotheses tested by
the real estate company?
a)
H
0:
μ
G–
μ
M≥0 versus
H
1:
μ
G–
μ
M<0
b)
H
0:
μ
G–
μ
M≤0 versus
H
1:
μ
G–
μ
M>0
c)
H
0:
μ
G–
μ
M=0 versus
H
1:
μ
G–
μ
M≠0
d) H0: X
G–X
M≥0 versus H1: X
G–X
M<0
10-8 Two-Sample Tests
26. Referring to Scenario 10-3, what is the estimated standard error of the difference between the 2
sample means?
a) 4.06
b) 5.61
c) 8.01
d) 16.00
27. Referring to Scenario 10-3, what is a point estimate for the mean of the sampling distribution of
the difference between the 2 sample means?
a) – 22
b) – 10
c) – 15
d) 0
28. Referring to Scenario 10-3, what is(are) the critical value(s) of the relevant hypothesis test if the
level of significance is 0.05?
a) t ≅ Z = – 1.645
b) t ≅ Z = ±1.96
c) t ≅ Z = – 1.96
d) t ≅ Z = – 2.080
29. Referring to Scenario 10-3, what is(are) the critical value(s) of the relevant hypothesis test if the
level of significance is 0.01?
a) t ≅ Z = – 1.96
b) t ≅ Z = ±1.96
c) t ≅ Z = – 2.080
d) t ≅ Z = – 2.33
Two-Sample Tests 10-9
30. Referring to Scenario 10-3, what is the test statistic for the difference between sample means?
a) – 8.75
b) – 3.69
c) – 2.33
d) – 1.96
31. Referring to Scenario 10-3, suppose
α
= 0.10. Which of the following represents the result of the
relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
32. Referring to Scenario 10-3, suppose
α
= 0.05. Which of the following represents the result of the
relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
33. Referring to Scenario 10-3, suppose
α
= 0.01. Which of the following represents the result of the
relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
10-10 Two-Sample Tests
34. Referring to Scenario 10-3, suppose
α
= 0.10. Which of the following represents the correct
conclusion?
a) There is not enough evidence that the mean amount of time families in Gotham have been
living in their current homes is less than families in Metropolis.
b) There is enough evidence that the mean amount of time families in Gotham have been
living in their current homes is less than families in Metropolis.
c) There is not enough evidence that the mean amount of time families in Gotham have been
living in their current homes is not less than families in Metropolis.
d) There is enough evidence that the mean amount of time families in Gotham have been
living in their current homes is not less than families in Metropolis.
35. Referring to Scenario 10-3, suppose
α
= 0.05. Which of the following represents the correct
conclusion?
a) There is not enough evidence that the mean amount of time families in Gotham have been
living in their current homes is less than families in Metropolis.
b) There is enough evidence that the mean amount of time families in Gotham have been
living in their current homes is less than families in Metropolis.
c) There is not enough evidence that the mean amount of time families in Gotham have been
living in their current homes is not less than families in Metropolis.
d) There is enough evidence that the mean amount of time families in Gotham have been
living in their current homes is not less than families in Metropolis.
36. Referring to Scenario 10-3, suppose
α
= 0.01. Which of the following represents the correct
conclusion?
a) There is not enough evidence that the mean amount of time families in Gotham have been
living in their current homes is less than families in Metropolis.
b) There is enough evidence that the mean amount of time families in Gotham have been
living in their current homes is less than families in Metropolis.
c) There is not enough evidence that the mean amount of time families in Gotham have been
living in their current homes is not less than families in Metropolis.
d) There is enough evidence that the mean amount of time families in Gotham have been
living in their current homes is not less than families in Metropolis.
Two-Sample Tests 10-11
37. Referring to Scenario 10-3, what is the 99% confidence interval estimate for the difference in the
two means?
38. Referring to Scenario 10-3, what is the 95% confidence interval estimate for the difference in the
two means?
SCENARIO 10-4
Two samples each of size 25 are taken from independent populations assumed to be normally
distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0
while the second sample has a mean of 33.0 and standard deviation of 4.0.
39. Referring to Scenario 10-6, the pooled (i.e., combined) variance is _______.
40. Referring to Scenario 10-4, the computed t statistic is _______.
41. Referring to Scenario 10-4, there are _______ degrees of freedom for this test.
42. Referring to Scenario 10-4, the critical values for a two-tail test of the null hypothesis of no
difference in the population means at the
α
= 0.05 level of significance are _______.
10-12 Two-Sample Tests
43. Referring to Scenario 10-4, a two-tail test of the null hypothesis of no difference would _______
(be rejected/not be rejected) at the
α
= 0.05 level of significance.
44. Referring to Scenario 10-4, the p-value for a two-tail test is _______.
45. Referring to Scenario 10-4, if you were interested in testing against the one-tail alternative that
μ
1>
μ
2 at the
α
= 0.01 level of significance, the null hypothesis would ______ (be rejected/not
be rejected).
46. Referring to Scenario 10-4, the p-value for a one-tail test (in the hypothesized direction) is
_______.
47. Referring to Scenario 10-4, what is the 99% confidence interval estimate for the difference in the
two means?
48. Referring to Scenario 10-4, what is the 95% confidence interval estimate for the difference in the
two means?
Two-Sample Tests 10-13
49. Referring to Scenario 10-4, what is the 90% confidence interval estimate for the difference in the
two means?
50. The t test for the mean difference between 2 related populations assumes that the
a) population sizes are equal.
b) sample variances are equal.
c) population of differences is approximately normal or sample sizes are large enough.
d) All of the above.
51. If we are testing for the difference between the means of 2 related populations with samples of n1
= 20 and n2 = 20, the number of degrees of freedom is equal to
a) 39.
b) 38.
c) 19.
d) 18.
52. In what type of test is the variable of interest the difference between the values of the
observations rather than the observations themselves?
a) A test for the equality of variances from 2 independent populations.
b) A test for the difference between the means of 2 related populations.
c) A test for the difference between the means of 2 independent populations.
d) All of the above.
10-14 Two-Sample Tests
53. In testing for differences between the means of 2 related populations where the variance of the
differences is unknown, the degrees of freedom are
a) n – 1.
b) n1 + n2 – 1.
c) n1 + n2 – 2.
d) n – 2.
54. In testing for differences between the means of two related populations, the null hypothesis is
a) 0: 2
D
H
μ
=.
b) 0: 0
D
H
μ
=.
c) 0: 0
D
H
μ
<.
d) 0: 0
D
H
μ
>.
55. In testing for the differences between the means of two related populations, the _______
hypothesis is the hypothesis of “no differences.”
56. In testing for the differences between the means of two related populations, you assume that the
differences follow a _______ distribution.
57. True or False: When testing for differences between the means of 2 related populations, you can
use either a one-tail or two-tail test.
Two-Sample Tests 10-15
58. True or False: A researcher is curious about the effect of sleep on students’ test performances. He
chooses 60 students and gives each two tests: one given after two hours’ sleep and one after eight
hours’ sleep. The test the researcher should use would be a related samples test.
59. True or False: Repeated measurements from the same individuals is an example of data collected
from two related populations.
60. True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed
an obstacle course both before and after basic training. To test whether any improvement
occurred, the instructor would use a t-distribution with 11 degrees of freedom.
61. True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed
an obstacle course both before and after basic training. To test whether any improvement
occurred, the instructor would use a t-distribution with 10 degrees of freedom.
SCENARIO 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business
test before and after the course. The results are given below.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
10-16 Two-Sample Tests
62. Referring to Scenario 10-5, the number of degrees of freedom is
a) 14.
b) 13.
c) 8.
d) 7.
63. Referring to Scenario 10-5, the value of the sample mean difference is _______ if the difference
scores reflect the results of the exam after the course minus the results of the exam before the
course.
a) 0
b) 50
c) 68
d) 400
64. Referring to Scenario 10-5, the value of the standard error of the difference scores is
a) 65.027
b) 60.828
c) 22.991
d) 14.696
65. Referring to Scenario 10-5, what is the critical value for testing at the 5% level of significance
whether the business school preparation course is effective in improving exam scores?
a) 2.365
b) 2.145
c) 1.761
d) 1.895
Two-Sample Tests 10-17
66. Referring to Scenario 10-5, at the 0.05 level of significance, the decision for this hypothesis test
would be:
a) reject the null hypothesis.
b) do not reject the null hypothesis.
c) reject the alternative hypothesis.
d) It cannot be determined from the information given.
67. Referring to Scenario 10-5, at the 0.05 level of significance, the conclusion for this hypothesis
test is that there is sufficient evidence that:
a) the business school preparation course does improve exam score.
b) the business school preparation course does not improve exam score.
c) the business school preparation course has no impact on exam score.
d) no conclusion can be drawn from the information given.
68. True or False: Referring to Scenario 10-5, you must assume that the population of difference
scores is normally distributed.
69. Referring to Scenario 10-5, the calculated value of the test statistic is ________.
70. Referring to Scenario 10-5, the p-value of the test statistic is ________.
10-18 Two-Sample Tests
71. True or False: Referring to Scenario 10-5, in examining the differences between related samples
we are essentially sampling from an underlying population of difference “scores.”
SCENARIO 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a
population of adult males using the diet. The weight of each individual in the sample is taken at the
start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences
in weight before versus after the diet follow a normal distribution, the t-test for related samples can be
used to determine if there was a significant decrease in the mean weight during this period. Suppose
the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard
deviation of differences computed as 6.0 pounds.
72. Referring to Scenario 10-6, the t test should be _______-tail.
73. Referring to Scenario 10-6, the computed t statistic is _______.
74. Referring to Scenario 10-6, there are _______ degrees of freedom for this test.
75. Referring to Scenario 10-6, the critical value for a one-tail test of the null hypothesis of no
difference at the
α
= 0.05 level of significance is _______.
Two-Sample Tests 10-19
76. Referring to Scenario 10-6, a one-tail test of the null hypothesis of no difference would _______
(be rejected/not be rejected) at the
α
= 0.05 level of significance.
77. Referring to Scenario 10-6, the p-value for a one-tail test is _______.
78. Referring to Scenario 10-6, if we were interested in testing against the two-tail alternative that
D
μ
is not equal to zero at the
α
= 0.05 level of significance, the null hypothesis would _______
(be rejected/not be rejected).
79. Referring to Scenario 10-6, the p-value for a two-tail is _______.
80. Referring to Scenario 10-6, what is the 95% confidence interval estimate for the mean difference
in weight before and after the diet?
81. Referring to Scenario 10-6, what is the 99% confidence interval estimate for the mean difference
in weight before and after the diet?
10-20 Two-Sample Tests
82. Referring to Scenario 10-6, what is the 90% confidence interval estimate for the mean difference
in weight before and after the diet?
SCENARIO 10-7
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.
In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices
on various identical materials. He wants to compare these prices with those of his primary supplier.
The data collected is presented in the table below, with some summary statistics presented (all of
these might not be necessary to answer the questions which follow). The buyer believes that the
differences are normally distributed and will use this sample to perform an appropriate test at a level
of significance of 0.01.
Primary Secondary
Material Supplier Supplier Difference
1 $55 $45 $10
2 $48 $47 $1
3 $31 $32 – $1
4 $83 $77 $6
5 $37 $37 $0
6 $55 $54 $1
Sum: $309 $292 $17
Sum of Squares: $17,573 $15,472 $139
83. Referring to Scenario 10-7, the hypotheses that the buyer should test are a null hypothesis that
________ versus an alternative hypothesis that ________.
84. Referring to Scenario 10-7, the test to perform is a
a) pooled-variance t test for differences between two means.
b) separate-variance t test for differences between two means.
c) Z test for the difference between two proportions.
d) paired t-test for the mean difference.
Two-Sample Tests 10-21
85. Referring to Scenario 10-7, the decision rule is to reject the null hypothesis if ________.
86. Referring to Scenario 10-7, the calculated value of the test statistic is ________.
87. Referring to Scenario 10-7, the p-value of the test statistic is ________.
88. True or False: Referring to Scenario 10-7, the null hypothesis should be rejected.
89. Referring to Scenario 10-7, the buyer should decide that the primary supplier is
a) overcharging because there is strong evidence that this is the case.
b) overcharging because there is insufficient evidence to prove otherwise.
c) not overcharging because there is insufficient evidence to prove otherwise.
d) not overcharging because there is strong evidence to prove otherwise.
90. Referring to Scenario 10-7, if the buyer had decided to perform a two-tail test, the p-value would
have been ________.
10-22 Two-Sample Tests
91. Referring to Scenario 10-7, what is the 99% confidence interval estimate for the mean difference
in prices?
92. Referring to Scenario 10-7, what is the 95% confidence interval estimate for the mean difference
in prices?
93. Referring to Scenario 10-7, what is the 90% confidence interval estimate for the mean difference
in prices?
94. When testing 01 2 11 2
: – 0 versus : – 0HH
ππ ππ
=≠
, the observed value of the Z test statistic
was found to be – 2.13. The p-value for this test is
a) 0.0166.
b) 0.0332.
c) 0.9668.
d) 0.9834.
95. When testing 01 2
: 0H
ππ
−≤
versus 11 2
: 0H
ππ
−>
, the observed value of the Z test statistic
was found to be – 2.13. The p-value for this test is
a) 0.0166.
b) 0.0332.
c) 0.9668.
d) 0.9834.
Two-Sample Tests 10-23
96. When testing 01 2
: 0H
ππ
−≥
versus 11 2
: 0H
ππ
−<
, the observed value of the Z test statistic
was found to be – 2.13. The p-value for this test is
a) 0.0166.
b) 0.0332.
c) 0.9668.
d) 0.9834.
97. Moving companies are required by the government to publish a Carrier Performance Report each
year. One of the descriptive statistics they must include is the annual percentage of shipments on
which a $50 or greater claim for loss or damage was filed. Suppose two companies, Econo-Move
and On-the-Move, each decide to estimate this figure by sampling their records, and they report
the data shown in the following table.
Econo-Move
On-the-Move
Total shipments sampled 900 750
Number of shipments with a claim ≥ $50 162 60
The owner of On-the-Move is hoping to use these data to show that the company is superior to
Econo-Move with regard to the percentage of claims filed. Which test would be used to properly
analyze the data in this experiment?
a) t test for the difference between two means
b) F test for the ratio of variances
c) Separate variance t test for the difference between two means
d) Z test for the difference between two proportions
10-24 Two-Sample Tests
98. The Wall Street Journal recently published an article indicating differences in perception of
sexual harassment on the job between men and women. The article claimed that women perceived
the problem to be much more prevalent than did men. One question asked of both men and
women was: “Do you think sexual harassment is a major problem in the American workplace?”
24% of the men compared to 62% of the women responded “Yes.” Assuming W designates
women’s responses and M designates men’s, what hypothesis should The Wall Street Journal test
in order to show that its claim is true?
a) H0: WM
ππ
− ≥ 0 versus H1: WM
ππ
−< 0
b) H0: WM
ππ
−≤ 0 versus H1: WM
ππ
−> 0
c) H0: WM
ππ
−= 0 versus H1: WM
ππ
−≠ 0
d) H0: WM
ππ
−≠ 0 versus H1: WM
ππ
−= 0
99. The Wall Street Journal recently ran an article indicating differences in perception of sexual
harassment on the job between men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question asked to both men and women
was: “Do you think sexual harassment is a major problem in the American workplace?” Some
24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and
200 men were interviewed. For a 0.01 level of significance, what is the critical value for the
rejection region?
a) 7.173
b) 7.106
c) 6.635
d) 2.33
100. The Wall Street Journal recently ran an article indicating differences in perception of sexual
harassment on the job between men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question asked to both men and women
was: “Do you think sexual harassment is a major problem in the American workplace?” Some
24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and
200 men were interviewed. What is the value of the test statistic?
a) 7.173
b) 7.106
c) 6.635
d) 2.33
Two-Sample Tests 10-25
101. The Wall Street Journal recently ran an article indicating differences in perception of sexual
harassment on the job between men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question asked to both men and women
was: “Do you think sexual harassment is a major problem in the American workplace?” Some
24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and
200 men were interviewed. Construct a 99% confidence interval estimate of the difference
between the proportion of women and men who think sexual harassment is a major problem in
the American workplace.
102. The Wall Street Journal recently ran an article indicating differences in perception of sexual
harassment on the job between men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question asked to both men and women
was: “Do you think sexual harassment is a major problem in the American workplace?” Some
24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and
200 men were interviewed. Construct a 95% confidence interval estimate of the difference
between the proportion of women and men who think sexual harassment is a major problem in
the American workplace.
103. The Wall Street Journal recently ran an article indicating differences in perception of sexual
harassment on the job between men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question asked to both men and women
was: “Do you think sexual harassment is a major problem in the American workplace?” Some
24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and
200 men were interviewed. Construct a 90% confidence interval estimate of the difference
between the proportion of women and men who think sexual harassment is a major problem in
the American workplace.
10-26 Two-Sample Tests
104. The Wall Street Journal recently ran an article indicating differences in perception of sexual
harassment on the job between men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question asked to both men and women
was: “Do you think sexual harassment is a major problem in the American workplace?” Some
24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and
200 men were interviewed. What conclusion should be reached?
a) Using a 0.01 level of significance, there is sufficient evidence to conclude that women
perceive the problem of sexual harassment on the job as much more prevalent than do
men.
b) There is insufficient evidence to conclude with at least 99% confidence that women
perceive the problem of sexual harassment on the job as much more prevalent than do
men.
c) There is no evidence of a significant difference between the men and women in their
perception.
d) More information is needed to draw any conclusions from the data set.
105. A powerful women’s group has claimed that men and women differ in attitudes about sexual
discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought
sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19
of the women did believe that sexual discrimination is a problem. Assuming W designates
women’s responses and M designates men’s, which of the following are the appropriate null and
alternative hypotheses to test the group’s claim?
a) H0: 0≤− WM
π
π
versus H1: 0>− WM
π
π
b) H0: 0≥− WM
π
π
versus H1: 0<− WM
π
π
c) H0: 0=− WM
π
π
versus H1: 0≠− WM
π
π
d) H0: 0≠− WM
π
π
≤ 0 versus H1: 0=− WM
π
π
Two-Sample Tests 10-27
106. A powerful women’s group has claimed that men and women differ in attitudes about sexual
discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought
sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19
of the women did believe that sexual discrimination is a problem. Find the value of the test
statistic.
a) Z = – 2.55
b) Z = – 0.85
c) Z = – 1.05
d) Z = – 1.20
107. A powerful women’s group has claimed that men and women differ in attitudes about sexual
discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought
sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19
of the women did believe that sexual discrimination is a problem. If the p-value turns out to be
0.035 (which is not the real value in this data set), then
a) at
α
= 0.05, you should fail to reject H0
b) at
α
= 0.04, you should reject H0
c) at
α
= 0.03, you should reject H0
d) None of the above would be correct statements.
108. A powerful women’s group has claimed that men and women differ in attitudes about sexual
discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought
sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19
of the women did believe that sexual discrimination is a problem. Construct a 99% confidence
interval estimate of the difference between the proportion of men and women who believe that
sexual discrimination is a problem.
10-28 Two-Sample Tests
109. A powerful women’s group has claimed that men and women differ in attitudes about sexual
discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought
sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19
of the women did believe that sexual discrimination is a problem. Construct a 95% confidence
interval estimate of the difference between the proportion of men and women who believe that
sexual discrimination is a problem.
110. A powerful women’s group has claimed that men and women differ in attitudes about sexual
discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought
sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19
of the women did believe that sexual discrimination is a problem. Construct a 90% confidence
interval estimate of the difference between the proportion of men and women who believe that
sexual discrimination is a problem.
111. If you wish to determine whether there is evidence that the proportion of items of interest is
higher in group 1 than in group 2, the appropriate test to use is
a) the Z test for the difference between two proportions.
b) the F test for the ratio of variances.
c) the pooled-variance t test for the difference between two proportions.
d) the F test for the difference between two proportions.
112. True or False: In testing the difference between two proportions using the normal distribution,
you may use a two-tail Z test.
Two-Sample Tests 10-29
113. If you wish to determine whether there is evidence that the proportion of items of interest is
higher in Group 1 than in Group 2, and the test statistic for Z = +2.07 where the difference is
defined as Group 1’s proportion minus Group 2’s proportion, the p-value is equal to ______.
114. If we wish to determine whether there is evidence that the proportion of items of interest is
higher in Group 1 than in Group 2, and the test statistic for Z = −2.07 where the difference is
defined as Group 1’s proportion minus Group 2’s proportion, the p-value is equal to ______.
SCENARIO 10-8
A few years ago, Pepsi invited consumers to take the “Pepsi Challenge.” Consumers were asked to
decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in
determining what factors played a role in people’s taste preferences. One of the factors studied was
the gender of the consumer. Below are the results of analyses comparing the taste preferences of men
and women with the proportions depicting preference for Pepsi.
Males: n = 109, pM = 0.422018 Females: n = 52, pF = 0.25
pM – pF = 0.172018 Z = 2.11825
115. Referring to Scenario 10-8, to determine if a difference exists in the taste preferences of men
and women, give the correct alternative hypothesis that Pepsi would test.
a) H1:
μ
M
–
μ
F
≠0
b) H1:
μ
M
–
μ
F
>0
c) H1:
M
F
ππ
− ≠ 0
d) H1:
M
F
ππ
−= 0
10-30 Two-Sample Tests
116. Referring to Scenario 10-8, suppose Pepsi wanted to test to determine if the males preferred
Pepsi more than the females. Using the test statistic given, compute the appropriate p-value for
the test.
a) 0.0171
b) 0.0340
c) 0.2119
d) 0.4681
117. Referring to Scenario 10-8, suppose Pepsi wanted to test to determine if the males preferred
Pepsi less than the females. Using the test statistic given, compute the appropriate p-value for the
test.
a) 0.0170
b) 0.0340
c) 0.9660
d) 0.9830
118. Referring to Scenario 10-8, suppose that the two-tail p-value was really 0.0734. State the proper
conclusion.
a) At
α
= 0.05, there is sufficient evidence to indicate the proportion of males preferring
Pepsi differs from the proportion of females preferring Pepsi.
b) At
α
= 0.10, there is sufficient evidence to indicate the proportion of males preferring
Pepsi differs from the proportion of females preferring Pepsi.
c) At
α
= 0.05, there is sufficient evidence to indicate the proportion of males preferring
Pepsi equals the proportion of females preferring Pepsi.
d) At
α
= 0.08, there is insufficient evidence to indicate the proportion of males preferring
Pepsi differs from the proportion of females preferring Pepsi.
119. Referring to Scenario 10-8, construct a 90% confidence interval estimate of the difference
between the proportion of males and females who prefer Pepsi.
Two-Sample Tests 10-31
120. Referring to Scenario 10-8, construct a 95% confidence interval estimate of the difference
between the proportion of males and females who prefer Pepsi.
121. Referring to Scenario 10-8, construct a 99% confidence interval estimate of the difference
between the proportion of males and females who prefer Pepsi.
SCENARIO 10-9
The following EXCEL output contains the results of a test to determine whether the proportions of
satisfied customers at two resorts are the same or different.
Hypothesized Difference 0
Level of Significance 0.05
Group 1
Number of Items of Interest 160
Sample Size 200
Group 2
Number of Items of Interest 172
Sample Size 250
Intermediate Calculations
Group 1 Proportion 0.8
Group 2 Proportion 0.688
Difference in Two Proportions 0.112
Average Proportion 0.737777778
Z Test Statistic 2.684103363
Two-Tail Test
Lower Critical Value -1.959963985
Upper Critical Value 1.959963985
p-Value 0.007272462
10-32 Two-Sample Tests
122. Referring to Scenario 10-9, allowing for 1% probability of committing a Type I error, what are
the decision and conclusion on testing whether there is any difference in the proportions of
satisfied customers in the two resorts?
a) Do not reject the null hypothesis; there is enough evidence to conclude that there is
significant difference in the proportions of satisfied guests at the two resorts.
b) Do not reject the null hypothesis; there is not enough evidence to conclude that there is
significant difference in the proportions of satisfied guests at the two resorts.
c) Reject the null hypothesis; there is enough evidence to conclude that there is significant
difference in the proportions of satisfied guests at the two resorts.
d) Reject the null hypothesis; there is not enough evidence to conclude that there is
significant difference in the proportions of satisfied guests at the two resorts.
123. Referring to Scenario 10-9, if you want to test the claim that “Resort 1 (Group 1) has a higher
proportion of satisfied customers compared to Resort 2 (Group 2)”, the p-value of the test will be
a) 0.007272
b) 0.00727/2
c) 2*(0.00727)
d) 1-(0.00727/2)
124. Referring to Scenario 10-9, if you want to test the claim that “Resort 1 (Group 1) has a lower
proportion of satisfied customers compared to Resort 2 (Group 2)”, you will use
a) a t-test for the difference between two proportions.
b) a Z-test for the difference between two proportions.
c) an F test for the difference between two proportions.
d) an F test for the ratio of two variances.
125. Referring to Scenario 10-9, construct a 99% confidence interval estimate of the difference in
the population proportion of satisfied customers between the two resorts.
Two-Sample Tests 10-33
126. Referring to Scenario 10-9, construct a 95% confidence interval estimate of the difference in
the population proportion of satisfied guests between the two resorts.
127. Referring to Scenario 10-9, construct a 90% confidence interval estimate of the difference in
the population proportion of satisfied customers between the two resorts.
SCENARIO 10-10
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-
improvement course would like such a course. The firm did a similar study 10 years ago in which
60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are
assumed to be independent random samples. Let 1
π
and 2
π
represent the true proportion of workers
who would like to attend a self-improvement course in the recent study and the past study,
respectively.
128. Referring to Scenario 10-11, if the firm wanted to test whether this proportion has changed
from the previous study, which represents the relevant hypotheses?
a) H0: 12
ππ
− = 0 versus H1: 12
ππ
−≠ 0
b) H0: 12
ππ
−≠ 0 versus H1: 12
ππ
−= 0
c) H0: 12
ππ
−≤ 0 versus H1: 12
ππ
−> 0
d) H0: 12
ππ
−≥ 0 versus H1: 12
ππ
−< 0
10-34 Two-Sample Tests
129. Referring to Scenario 10-10, if the firm wanted to test whether a greater proportion of workers
would currently like to attend a self-improvement course than in the past, which represents the
relevant hypotheses?
a) H0: 12
ππ
−= 0 versus H1: 12
ππ
−≠ 0
b) H0: 12
ππ
−≠ 0 versus H1: 12
ππ
−= 0
c) H0: 12
ππ
−≤ 0 versus H1: 12
ππ
−> 0
d) H0: 12
ππ
−≥ 0 versus H1: 12
ππ
−< 0
130. Referring to Scenario 10-10, what is the point estimate for the difference between the two
population proportions?
a) 0.06
b) 0.10
c) 0.15
d) 0.22
131. Referring to Scenario 10-10, what is/are the critical value(s) when performing a Z test on
whether population proportions are different if
α
= 0.05?
a) ± 1.645
b) ± 1.96
c) −1.96
d) ± 2.08
132. Referring to Scenario 10-10, what is/are the critical value(s) when testing whether population
proportions are different if
α
= 0.10?
a) ± 1.645
b) ± 1.96
c) -1.96
d) ± 2.08
Two-Sample Tests 10-35
133. Referring to Scenario 10-10, what is/are the critical value(s) when testing whether the current
population proportion is higher than before if
α
= 0.05?
a) ±1.645
b) + 1.645
c) ±1.96
d) + 1.96
134. Referring to Scenario 10-10, what is the estimated standard error of the difference between the
two sample proportions?
a) 0.629
b) 0.500
c) 0.055
d) 0
135. Referring to Scenario 10-10, what is the value of the test statistic to use in evaluating the
alternative hypothesis that there is a difference in the two population proportions?
a) 4.335
b) 1.96
c) 1.093
d) 0
10-36 Two-Sample Tests
136. Referring to Scenario 10-10, the company tests to determine at the 0.05 level whether the
population proportion has changed from the previous study. Which of the following is correct?
a) Reject the null hypothesis and conclude that the proportion of employees who are
interested in a self-improvement course has changed over the intervening 10 years.
b) Do not reject the null hypothesis and conclude that the proportion of employees who are
interested in a self-improvement course has not changed over the intervening 10 years.
c) Reject the null hypothesis and conclude that the proportion of employees who are
interested in a self-improvement course has increased over the intervening 10 years.
d) Do not reject the null hypothesis and conclude that the proportion of employees who are
interested in a self-improvement course has increased over the intervening 10 years.
137. Referring to Scenario 10-10, construct a 99% confidence interval estimate of the difference in
proportion of workers who would like to attend a self-improvement course in the recent study and
the past study.
138. Referring to Scenario 10-10, construct a 95% confidence interval estimate of the difference in
proportion of workers who would like to attend a self-improvement course in the recent study and
the past study.
139. Referring to Scenario 10-10, construct a 90% confidence interval estimate of the difference in
proportion of workers who would like to attend a self-improvement course in the recent study and
the past study.
Two-Sample Tests 10-37
SCENARIO 10-11
The dean of a college is interested in the proportion of graduates from his college who have a job
offer on graduation day. He is particularly interested in seeing if there is a difference in this
proportion for accounting and economics majors. In a random sample of 100 of each type of major at
graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the
accounting majors are designated as “Group 1” and the economics majors are designated as “Group
2,” perform the appropriate hypothesis test using a level of significance of 0.05.
140. Referring to Scenario 10-12, the hypotheses the dean should use are:
a) H0: 12
ππ
− = 0 versus H1: 12
ππ
−≠ 0
b) H0: 12
ππ
−≠ 0 versus H1: 12
ππ
−= 0
c) H0: 12
ππ
−≤ 0 versus H1: 12
ππ
−> 0
d) H0: 12
ππ
−≥ 0 versus H1: 12
ππ
−< 0
141. Referring to Scenario 10-11, the null hypothesis will be rejected if the test statistic is ________.
142. Referring to Scenario 10-11, the value of the test statistic is ________.
143. Referring to Scenario 10-11, the p-value of the test is ________.
KEYWORDS: Z test for the difference in proportions, p-value
144. True or False: Referring to Scenario 10-11, the null hypothesis should be rejected.
10-38 Two-Sample Tests
145. True or False: Referring to Scenario 10-11, the same decision would be made with this test if
the level of significance had been 0.01 rather than 0.05.
146. True or False: Referring to Scenario 10-11, the same decision would be made with this test if
the level of significance had been 0.10 rather than 0.05.
147. Referring to Scenario 10-11, construct a 99% confidence interval estimate of the difference in
proportion between accounting majors and economic majors who have a job offer on graduation
day.
148. Referring to Scenario 10-11, construct a 95% confidence interval estimate of the difference in
proportion between accounting majors and economic majors who have a job offer on graduation
day.
149. Referring to Scenario 10-11, construct a 90% confidence interval estimate of the difference in
proportion between accounting majors and economic majors who have a job offer on graduation
day.
Two-Sample Tests 10-39
SCENARIO 10-12
A quality control engineer is in charge of the manufacture of USB flash drives. Two different
processes can be used to manufacture the flash drives. He suspects that the Kohler method produces a
greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the
Russell flash drives and finds that 27 and 18 of them, respectively, are defective. If Kohler is
designated as “Group 1” and Russell is designated as “Group 2,” perform the appropriate test at a
level of significance of 0.01.
150. Referring to Scenario 10-12, the hypotheses that should be tested are:
a) H0: 12
ππ
−= 0 versus H1: 12
ππ
−≠ 0
b) H0: 12
ππ
−≠ 0 versus H1: 12
ππ
−= 0
c) H0: 12
ππ
−≤ 0 versus H1: 12
ππ
−> 0
d) H0: 12
ππ
−≥ 0 versus H1: 12
ππ
−< 0
151. Referring to Scenario 10-12, the null hypothesis will be rejected if the test statistic is ________.
152. Referring to Scenario 10-12, the value of the test statistic is ________.
153. Referring to Scenario 10-12, the p-value of the test is ________.
154. True or False: Referring to Scenario 10-12, the null hypothesis should be rejected.
10-40 Two-Sample Tests
155. True or False: Referring to Scenario 10-12, the same decision would be made with this test if
the level of significance had been 0.05 rather than 0.01.
156. True or False: Referring to Scenario 10-12, the same decision would be made if this had been a
two-tail test at a level of significance of 0.01.
157. Referring to Scenario 10-12, construct a 90% confidence interval estimate of the difference in
proportion between the Kohler and Russell flash drives that are defective.
158. Referring to Scenario 10-12, construct a 95% confidence interval estimate of the difference in
proportion between the Kohler and Russell flash drives that are defective.
159. Referring to Scenario 10-12, construct a 99% confidence interval estimate of the difference in
proportion between the Kohler and Russell flash drives that are defective.
160. When testing for the difference between 2 population variances with sample sizes of n1 = 8 and
n2 = 10, where n1 has the larger variance, the number of degrees of freedom are
a) 8 and 10.
b) 7 and 9.
c) 18.
d) 16.
Two-Sample Tests 10-41
161. The statistical distribution used for testing the difference between two population variances is
the ___ distribution.
a) t
b) standardized normal
c) binomial
d) F
162. The test for the equality of two population variances is based on
a) the difference between the 2 sample variances.
b) the ratio of the 2 sample variances.
c) the difference between the 2 population variances.
d) the difference between the sample variances divided by the difference between the
sample means.
163. True or False: The F test used for testing the difference in two population variances is always a
one-tail test.
164. True or False: The test for the equality of two population variances assumes that each of the
two populations is normally distributed.
165. True or False: The F distribution is symmetric.
10-42 Two-Sample Tests
166. True or False: The F distribution can only have positive values.
167. True or False: F tests are one-tail tests.
SCENARIO 10-13
The amount of time required to reach a customer service representative has a huge impact on
customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a
difference in the mean amounts of time required to reach a customer service representative between
two hotels. Assume that the population variances in the amount of time for the two hotels are not
equal.
t-Test: Two-Sample Assuming Unequal Variances
Hotel 1 Hotel 2
Mean 2.214 2.0115
Variance 2.951657 3.57855
Observations 20 20
Hypothesized Mean Difference 0
df 38
t Stat 0.354386
P(T<=t) one-tail 0.362504
t Critical one-tail 1.685953
P(T<=t) two-tail 0.725009
t Critical two-tail 2.024394
168. Referring to Scenario 10-13, which of the following represents the relevant hypotheses tested?
a) 0– : versus 0– : 10 <≥ IIIIII HH
μ
μ
μ
μ
b) 0– : versus 0– : 10 >≤ IIIIII HH
μ
μ
μ
μ
c) 0– : versus 0– : 10 ≠= IIIIII HH
μ
μ
μ
μ
d) 0– : versus 0– : 10 =≠ IIIIII HH
μ
μ
μ
μ
Two-Sample Tests 10-43
169. Referring to Scenario 10-13, what is(are) the critical value(s) of the relevant hypothesis test if
the level of significance is 0.05?
a) 1.6860
b) ±1.6860
c) 2.0244
d) ±2.0244
170. Referring to Scenario 10-13, what is(are) the critical value(s) of the relevant hypothesis test if
the level of significance is 0.10?
a) 1.6860
b) ±1.6860
c) 2.0244
d) ±2.0244
171. Referring to Scenario 10-13, what is the standardized value of the estimate of the mean of the
sampling distribution for the difference between sample means?
a) 0.2025
b) 0.3544
c) 2.0115
d) 2.2140
172. Referring to Scenario 10-13, what is the value of the test statistic?
a) 0.2025
b) 0.3544
c) 2.0115
d) 2.2140
10-44 Two-Sample Tests
173. Referring to Scenario 10-13, what is the smallest level of significance at which the null
hypothesis will still not be rejected?
a) 0.05
b) 0.10
c) 0.3625
d) 0.7250
174. Referring to Scenario 10-13, suppose
α
= 0.10. Which of the following represents the result of
the relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
175. Referring to Scenario 10-13, suppose
α
= 0.05. Which of the following represents the result of
the relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
176. Referring to Scenario 10-13, suppose
α
= 0.10. Which of the following represents the correct
conclusion?
a) There is not enough evidence of a difference in the mean amounts of time between the
two hotels.
b) There is enough evidence of a difference in the mean amounts of time between the two
hotels.
c) There is not enough evidence that the mean amounts of time for the two hotels are the
same.
d) There is enough evidence that the mean amounts of time for the two hotels are the same.
Two-Sample Tests 10-45
177. Referring to Scenario 10-13, suppose
α
= 0.05. Which of the following represents the correct
conclusion?
a) There is not enough evidence of a difference in the mean amounts of time between the
two hotels.
b) There is enough evidence of a difference in the mean amounts of time between the two
hotels.
c) There is not enough evidence that the mean amounts of time for the two hotels are the
same.
d) There is enough evidence that the mean amounts of time for the two hotels are the same.
178. Referring to Scenario 10-13, what is the 95% confidence interval estimate for the difference in
the two means if the two population variances are assumed to be the same?
179. Referring to Scenario 10-13, state the null and alternative hypotheses for testing if there is
evidence of a difference in the variabilities of the amount of time required to reach a customer
service representative between the two hotels.
a) 0– : versus 0– : 22
1
22
0<≥ IIIIII HH
σσσσ
b) 0– : versus 0– : 22
1
22
0>≤ IIIIII HH
σσσσ
c) 0– : versus 0– : 22
1
22
0≠= IIIIII HH
σσσσ
d) 0– : versus 0– : 22
1
22
0=≠ IIIIII HH
σσσσ
180. Referring to Scenario 10-13, what is the value of the test statistic for testing if there is evidence
of a difference in the variabilities of the amount of time required to reach a customer service
representative between the two hotels?
10-46 Two-Sample Tests
181. Referring to Scenario 10-13, what assumptions are necessary for testing if there is evidence of a
difference in the variabilities of the amount of time required to reach a customer service
representative between the two hotels to be valid?
a) Both sampled populations are normally distributed.
b) Both samples are random and independent.
c) Neither (a) nor (b) is necessary.
d) Both (a) and (b) are necessary.
182. Referring to Scenario 10-13, what is the critical value for testing if there is evidence of a
difference in the variabilities of the amount of time required to reach a customer service
representative between the two hotels at the 5% level of significance?
183. Referring to Scenario 10-13, what is the largest level of significance at which a test on a
difference in the variabilities of the amount of time required to reach a customer service
representative between the two hotels will not be rejected?
184. Referring to Scenario 10-13, suppose
α
= 0.05. Which of the following represents the result of
the test on a difference in the variabilities of the amount of time required to reach a customer
service representative between the two hotels?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
Two-Sample Tests 10-47
185. Referring to Scenario 10-13, suppose
α
= 0.05. Which of the following represents the correct
conclusion for a test on a difference in the variabilities of the amount of time required to reach a
customer service representative between the two hotels?
a) There is no evidence of a difference in the variabilities of the amount of time required to
reach a customer service representative between the two hotels.
b) There is evidence of a difference in the variabilities of the amount of time required to
reach a customer service representative between the two hotels.
c) There is no evidence that the variabilities of the amount of time required to reach a
customer service representative between the two hotels are the same.
d) There is evidence that the variabilities of the amount of time required to reach a customer
service representative between the two hotels are the same.
SCENARIO 10-14
The use of preservatives by food processors has become a controversial issue. Suppose two
preservatives are extensively tested and determined safe for use in meats. A processor wants to
compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are
treated with preservative I and 15 are treated with preservative II, and the number of hours until
spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table
below.
Preservative I Preservative II
X
I = 106.4 hours
X
II = 96.54 hours
S
I = 10.3 hours S II = 13.4 hours
186. Referring to Scenario 10-14, state the null and alternative hypotheses for testing if the
population variances differ for preservatives I and II.
a) 0– : versus 0– : 22
1
22
0<≥ IIIIII HH
σσσσ
b) 0– : versus 0– : 22
1
22
0>≤ IIIIII HH
σσσσ
c) 0– : versus 0– : 22
1
22
0≠= IIIIII HH
σσσσ
d) 0– : versus 0– : 22
1
22
0=≠ IIIIII HH
σσσσ
187. Referring to Scenario 10-14, what is the value of the test statistic for testing if the population
variances differ for preservatives I and II?
10-48 Two-Sample Tests
188. Referring to Scenario 10-14, what assumptions are necessary for testing if the population
variances differ for preservatives I and II?
a) Both sampled populations are normally distributed.
b) Both samples are random and independent.
c) Neither (a) nor (b) is necessary.
d) Both (a) and (b) are necessary.
189. Referring to Scenario 10-14, what is the critical value for testing if the population variances
differ for preservatives I and II at the 5% level of significance?
190. Referring to Scenario 10-14, what is the largest level of significance at which a test of whether
the population variances differ for preservatives I and II will not be rejected?
191. Referring to Scenario 10-14, suppose
α
= 0.05. Which of the following represents the result of
the relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
Two-Sample Tests 10-49
192. Referring to Scenario 10-14, suppose
α
= 0.05. Which of the following represents the correct
conclusion?
a) There is no evidence of a difference in the population variances between preservatives I
and II.
b) There is evidence of a difference in the population variances between preservatives I and
II.
c) There is no evidence that the population variances between preservatives I and II are the
same.
d) There is evidence that the population variances between preservatives I and II are the
same.
SCENARIO 10-15
The table below presents the summary statistics for the starting annual salaries (in thousands of
dollars) for individuals entering the public accounting and financial planning professions.
Sample I (public accounting): 160.35X=, 13.25S=, 112n=
Sample II (financial planning): 258.20X=, 22.48S=, 214n=
Test whether the mean starting annual salaries for individuals entering the public accounting
professions is higher than that of financial planning assuming that the two population variances are
the same.
193. Referring to Scenario 10-15, which of the following represents the relevant hypotheses tested?
a) 01 2 11 2
: – 0 versus : – 0HH
μμ μμ
≥<
b) 01 2 11 2
: – 0 versus : – 0HH
μμ μμ
≤>
c) 01 2 11 2
: – 0 versus : – 0HH
μμ μμ
=≠
d) 01 2 11 2
: – 0 ver sus : – 0HH
μμ μμ
≠=
194. Referring to Scenario 10-15, what is(are) the critical value(s) of the relevant hypothesis test if
the level of significance is 0.05?
10-50 Two-Sample Tests
195. Referring to Scenario 10-15, what is(are) the critical value(s) of the relevant hypothesis test if
the level of significance is 0.10?
196. Referring to Scenario 10-15, what is the value of the test statistic?
197. Referring to Scenario 10-15, what is the smallest level of significance at which the null
hypothesis will still not be rejected?
198. Referring to Scenario 10-15, suppose
α
= 0.10. Which of the following represents the result of
the relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
199. Referring to Scenario 10-15, suppose
α
= 0.01. Which of the following represents the result of
the relevant hypothesis test?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
Two-Sample Tests 10-51
200. Referring to Scenario 10-15, suppose
α
= 0.10. Which of the following represents the correct
conclusion?
a) There is not enough evidence that the mean starting annual salaries for individuals
entering the public accounting professions is not higher than that of financial planning.
b) There is not enough evidence that the mean starting annual salaries for individuals
entering the public accounting professions is not higher than that of financial planning.
c) There is not enough evidence that the mean starting annual salaries for individuals
entering the public accounting professions is higher than that of financial planning.
d) There is enough evidence that the mean starting annual salaries for individuals entering
the public accounting professions is higher than that of financial planning.
201. Referring to Scenario 10-15, suppose
α
= 0.01. Which of the following represents the correct
conclusion?
a) There is not enough evidence that the mean starting annual salaries for individuals
entering the public accounting professions is not higher than that of financial planning.
b) There is not enough evidence that the mean starting annual salaries for individuals
entering the public accounting professions is not higher than that of financial planning.
c) There is not enough evidence that the mean starting annual salaries for individuals
entering the public accounting professions is higher than that of financial planning.
d) There is enough evidence that the mean starting annual salaries for individuals entering
the public accounting professions is higher than that of financial planning.
202. Referring to Scenario 10-15, what is the 95% confidence interval estimate for the difference in
the two means?
203. Referring to Scenario 10-15, what additional assumption is needed for the test to be valid?
a) The two sample sizes have to be equal.
b) The two population sizes have to be equal.
c) The two population means have to be the same.
d) The population distributions of the two annual salaries have to be normal.
10-52 Two-Sample Tests
204. Referring to Scenario 10-15, state the null and alternative hypotheses for testing whether there
is evidence of a difference in the variances of the starting annual salaries.
a) 22 22
01 2 11 2
: – 0 ve rsus : – 0HH
σσ σσ
≥<
b) 22 22
01 2 11 2
: – 0 ve rsus : – 0HH
σσ σσ
≤>
c) 22 22
01 2 11 2
: – 0 versus : – 0HH
σσ σσ
=≠
d) 22 22
01 2 11 2
: – 0 v er sus : – 0HH
σσ σσ
≠=
205. Referring to Scenario 10-15, what is the value of the test statistic for testing whether there is
evidence of a difference in the variances?
206. Referring to Scenario 10-15, what assumptions are necessary for testing whether there is
evidence of a difference in the variances to be valid?
a) Both sampled populations are normally distributed.
b) Both samples are random and independent.
c) Neither (a) nor (b) is necessary.
d) Both (a) and (b) are necessary.
207. Referring to Scenario 10-15, what is the critical value for testing whether there is evidence of a
difference in the variances at the 5% level of significance?
208. Referring to Scenario 10-15, what is the highest level of significance at which a test on a
difference in the variances will not be rejected?
Two-Sample Tests 10-53
209. Referring to Scenario 10-15, suppose
α
= 0.05. Which of the following represents the result of
the test on a difference in the variances?
a) The alternative hypothesis is rejected.
b) The null hypothesis is rejected.
c) The null hypothesis is not rejected.
d) Insufficient information exists on which to make a decision.
210. Referring to Scenario 10-15, suppose
α
= 0.05. Which of the following represents the correct
conclusion for a test on a difference in the variances?
a) There is no evidence of a difference in the variances.
b) There is evidence of a difference in the variances.
c) There is no evidence that the variances are the same.
d) There is evidence that variances are the same.