Chapter 11
Two Samples Tests of
Hypothesis
True/False
1. If the null hypothesis states that there is
no difference between the mean income of males and the mean income of females,
then the test is one-tailed.
Answer:False
Difficulty: Easy Goal: 1
AACSB: MD
2. If the null hypothesis states that there is
no difference between the mean net income retail stores in Chicago and New York
City, then the test is two-tailed.
Answer:True
Difficulty: Easy Goal: 1
3. If we are testing for the difference between
two population means, it is assumed that the sample observations from one
population are independent of the sample observations from the other
population.
Answer:True
Difficulty: Easy Goal: 1
4. If we are testing for the difference between
two population proportions, it is assumed that the two populations are
approximately normal and have equal variances.
Answer:False
Difficulty: Easy Goal: 2
5. If we are testing for the difference between
two population proportions, it is assumed that the two samples are large enough
that the binomial distribution can be approximated by the normal distribution.
Answer:True
Difficulty: Easy Goal: 2
AACSB: AS
6. When sample sizes are less than 30, a test
for the differences between two population means has n–1 degrees of
freedom.
Answer:False
Difficulty: Easy Goal: 1
7. If we are testing for the difference between
two population means and assume that the two populations have equal but unknown
standard deviations, then the test has (n1 + n2 – 2) degrees of freedom.
Answer:True Difficulty: Easy Goal: 1
AACSB: AS
8. If we are testing for the difference between
two population means and assume that the two populations have equal but unknown
standard deviations, the variances are pooled to compute the best estimated
variance.
Answer:True Difficulty: Easy Goal: 1
9. If we are testing for the difference between
two population means and assume that the two populations have unequal and
unknown standard deviations, the degrees of freedom for the test statistic must
be computed or calculated.
Answer:True Difficulty: Easy Goal: 1
10. If we are testing for the difference between
two population means and assume that the two populations have unequal and
unknown standard deviations, the variances are pooled to compute the best
estimated variance.
Answer:False Difficulty: Easy Goal: 1
AACSB: REF
11. If samples taken from two populations are not
independent, then a test of paired differences is applied.
Answer:True
Difficulty: Easy Goal: 3
12. The paired difference test has (n1 + n2 – 2) degrees of freedom.
Answer:False
Difficulty: Easy Goal: 3
13. When testing for the difference between two
dependent samples, n1 = n2.
Answer:True
Difficulty: Easy Goal: 3
14. We use the pooled estimate of the proportion
in testing the difference between two population proportions.
Answer:True
Difficulty: Medium Goal: 2
15. The pooled estimate of the proportion is
found by dividing the total number of samples by the total number of successes.
Answer:False
Difficulty: Medium Goal: 2
16. The paired t test is especially
appropriate when the sample sizes of two groups are the same.
Answer:False
Difficulty: Easy Goal: 3
17. A committee studying employer-employee relations
proposed that each employee would rate his or her immediate supervisor and in
turn the supervisor would rate each employee. To find reactions regarding the
proposal, 120 office personnel and 160 plant personnel were selected at random. Seventy-eight of the office personnel and 90
of the plant personnel were in favor of the proposal. Computed z = 1.48. At the 0.05 level,
it was concluded that there is sufficient evidence to support the belief that
the proportion of office personnel in favor of the proposal is greater than
that of the plant personnel.
Answer:False
Difficulty: Hard Goal: 2
18. A statistics professor wants to compare
grades of two different groups of students taking the same course in two
different sections. This is an example
of a paired sample.
Answer:False
Difficulty: Easy Goal: 4
19. In one class, a statistics professor wants to
compare grades on the first and second exams. This is an example of paired or
dependent observations.
Answer:True
Difficulty: Easy Goal: 4
Multiple Choice
20. If
the decision is to reject the null hypothesis of no difference between two
population parameters, at the 5% level of significance, what are examples of
the alternate hypothesis and rejection region?
A) 
B) 
C) 
D) 
Answer:B Difficulty: Hard Goal: 2
21. A
poll of 400 people from Dobbs Ferry showed 250 preferred chocolate raspberry
coffee while 170 out of 350 in Irvington preferred the same flavor. To test the hypothesis that there is no
difference in preferences in the two villages, what is the alternate
hypothesis?
A) 
B) 
C) 
D) 
Answer:D Difficulty: Medium Goal: 2
22. If
the null hypothesis that two means are equal is true, where will 97% of the
computed z-values lie between?
A) 
2.58
B) 2.33
C) 2.17
D) 2.07
Answer:C Difficulty: Medium Goal: 1
AACSB: AS
23. How is a pooled estimate of the population
proportion represented?
A) pc
B) z
C) 
D) n
Answer:A Difficulty: Medium Goal: 2
24. Suppose we are testing the difference between
two proportions at the 0.05 level of significance. If the computed z is –1.07, what is
our decision?
A) Reject the null hypothesis
B) Do not reject the null hypothesis
C) Take a larger sample
D) Reserve judgment
Answer:B Difficulty: Medium Goal: 2
AACSB: AS
25. The
net weights of a sample of bottles filled by a machine manufactured by Edne,
and the net weights of a sample filled by a similar machine manufactured by
Orno, Inc., are (in grams):
Edne: 5, 8, 7, 6, 9 and 7
Orno:
8, 10, 7, 11, 9, 12, 14 and 9
Testing
the claim at the 0.05 level that the mean weight of the bottles filled by the
Orno machine is greater than the mean weight of the bottles filled by the Edne
machine, what is the critical value? Assume equal standard deviations for both
samples.
A) 2.179
B) 2.145
C) 1.782
D) 1.761
Answer:C Difficulty: Hard Goal: 1
26. A
hypothesis will test that two population means are equal. A sample of 10 with a standard deviation of 3
is selected from the first population and a sample of 15 with a standard
deviation of 8 from the second population.
The standard deviations are not equal.
Testing the claim at the 0.01 level, what is the critical value? Assume unequal
standard deviations.
A) 2.845
B) 2.787
C) 2.807
D) 2.977
Answer:A Difficulty: Hard Goal: 1
27. Which of the following conditions must be met
to conduct a test for the difference in two sample means?
A) Data must be at least of interval scale
B) Populations must be normal
C) Variances in the two populations must be
equal
D) A and B correct
E) A, B, and C are correct
Answer:D Difficulty: Medium Goal: 1
28. When
is it appropriate to use the paired difference t-test?
A) Four samples are compared at once
B) Any two samples are compared
C) Two independent samples are compared
D) Two dependent samples are compared
Answer:D Difficulty: Medium Goal: 3
29. Using
two independent samples, two population means are compared to determine if a
difference exists. The population
standard deviations are equal. The
number in the first sample is fifteen and the number in the second sample is
twelve. How many degrees of freedom are
associated with the critical value?
A) 24
B) 25
C) 26
D) 27
Answer:B Difficulty: Medium Goal: 1
30. Administering
the same test to a group of 15 students and a second group of 15 students to
see which group scores higher is an example of
A) a one sample test of means.
B) a two sample test of means.
C) a paired t-test.
D) a test of proportions.
Answer:B Difficulty: Medium Goal: 1
AACSB: AS
31. What
is the critical value for a one-tailed hypothesis test in which a null
hypothesis is tested at the 5% level of significance based on two samples, both
sample sizes are 13? Assume the
population standard deviations are equal.
A) 1.708
B) 1.711
C) 2.060
D) 2.064
Answer:B Difficulty: Medium Goal: 1
32. What is the critical value for a one-tailed
hypothesis test in which a null hypothesis is tested at the 5% level of significance
based on two samples, both sample sizes are 13?
The standard deviations for the samples are 5 and 7. Assume the population standard deviations are
unequal.
A) 2.064
B) 1.711
C) 2.074
D) 1.717
Answer:D Difficulty: Hard Goal: 1
33. If
two samples are used in a hypothesis test for which the combined degrees of
freedom is 24, which one of the following is NOT true about the two sample
sizes? Assume the population standard deviations are equal.
A) Sample A = 11; sample B = 13
B) Sample A = 12; sample B = 14
C) Sample A = 13; sample B = 13
D) Sample A = 10; sample B = 16
E) Cannot determine from the above information
Answer:A Difficulty: Hard Goal: 1
34. If
two samples, one of size 14 and the second of size 13, are used to test the
difference between population means, how many degrees of freedom are used to
find the critical value? Assume the population standard deviations are equal.
A) 27
B) 26
C) 25
D) 14
E) 13
Answer:C Difficulty: Hard Goal: 1
35. 20
randomly selected statistics students were given 15 multiple-choice questions
and 15 open-ended questions – all on the same material. The professor was interested in determining
which type of questions the students scored higher. This experiment is an example of
A) a one sample test of means.
B) a two sample test of means.
C) a paired t-test.
D) a test of proportions.
Answer:C Difficulty: Medium Goal: 3
Use the following to
answer questions 35-36:
Of 250 adults who
tried a new multi-grain cereal, “Wow!”, 187 rated it excellent; of 100 children
sampled, 66 rated it excellent.
36. Using the 0.1 significance level and the
alternate hypothesisp1 not equal top2, what is the null hypothesis?
A) 
B) 
C) 
D) None of the above
Answer:C Difficulty: Medium Goal: 2
37. What
test statistic should we use?
A) z-statistic
B) Right one-tailed test
C) Left one-tailed test
D) Two-tailed test
Answer:A Difficulty: Medium Goal: 2
Use the following to
answer questions 38-45:
A national
manufacturer of ball bearings is experimenting with two different processes for
producing precision ball bearings. It is
important that the diameters be as close as possible to an industry
standard. The output from each process
is sampled and the average error from the industry standard is calculated. The results are presented below.
The
researcher is interested in determining whether there is evidence that the two
processes yield different average errors. Assume that the population standard deviations
are equal.
38. What
is the null hypothesis?
A) 
.
B) 
.
C) 
.
D) 
.
Answer:A Difficulty: Medium Goal: 1
39. What is the alternate hypothesis?
A) .
B) .
C) .
D) .
Answer:B Difficulty: Medium Goal: 1
40. What is the degrees of freedom?
A) 10
B) 13
C) 26
D) 24
Answer:D Difficulty: Medium Goal: 1
41. What
is the critical t value at the 1% level of significance?
A) +2.779
B) –2.492
C) 
1.711
D) 2.797
Answer:D Difficulty: Medium Goal: 1
42. What
is the computed value of t?
A) +2.797
B) –2.797
C) –13.70
D) +13.70
Answer:C Difficulty: Hard Goal: 1
43. What
is the decision at the 1% level of significance?
A) Reject the null hypothesis and conclude the
means are different.
B) Reject the null hypothesis and conclude the means
are the same.
C) Fail to reject the null hypothesis and
conclude the means are the same.
D) Fail to reject the null hypothesis and
conclude the means are different.
Answer:A Difficulty: Hard Goal: 1
44. Assume
calculated tto be +2.70, at the 0.01 level of significance what would
be the decision?
A) Reject the null hypothesis and conclude the
means are different.
B) Reject the null hypothesis and conclude the
means are the same.
C) Fail to reject the null hypothesis and
conclude the means are the same.
D) Fail to reject the null hypothesis and
conclude the means are different.
Answer:C Difficulty: Hard Goal: 1
45. This example is what type of test?
A) One sample test of means.
B) Two sample test of means.
C) Paired t-test.
D) Test of proportions.
Answer:B Difficulty: Medium Goal: 1
Use the following to
answer questions 46-48:
The results of a
mathematics placement exam at Mercy College for two campuses is as follows:
46. What
is the null hypothesis if we want to test the hypothesis that the mean score on
Campus 1 is higher than on Campus 2?
A) 
.
B) 
.
C) 
.
D) 
.
E) None of the above
Answer:E Difficulty: Medium Goal: 1
47. What
is the computed value of the test statistic?
A) 9.3
B) 2.6
C) 3.4
D) 1.9
Answer:C Difficulty: Hard Goal: 1
48. Given
that the two population standard deviations are known, what is the p-value if
the computed test statistic is 4.1?
A) 1.0
B) 0.0
C) 0.05
D) 0.95
Answer:B Difficulty: Medium Goal: 2
Fill-in-the-Blank
49. What
is the purpose of pooling the sample variances when testing the difference
between two population means?
___________
Answer:To compute a single estimate of the
population variance. Difficulty: Medium Goal: 1
50. What is the critical value of t for a
two-tail test of the difference of two means, a level of significance of 0.10
and sample sizes of seven and fifteen? Assume equal population standard
deviations. _________
Answer:1.734 Difficulty: Medium Goal: 1
51. What
is the critical value of t for the claim that the difference of two
means is less than zero witha = 0.025 and sample sizes of nine and seven? Assume equal population
standard deviations. _________
Answer:-2.179
Difficulty: Medium Goal: 1
Use the following to
answer questions 52-55:
A study by a bank
compared the average savings of customers who were depositors for three years
or less, with those who had been depositors for more than three years. The results of a sample are:
52. Assuming
that the financial officer wants to show that there is a difference in the
average savings balance between the two classes of depositors, what is the null
hypothesis? _____________________
Answer:
Difficulty:Medium Goal: 2
53. For
= 0.05, what is the critical value of z?
___________
Answer:1.96 Difficulty: Medium Goal: 1
54. What
is the computed test statistic? ______________
Answer:11.00
Difficulty: Hard Goal: 1
55. What
is the p-value ifa = .05 and the test statistic is 3.15? _____
Answer:approximately 0.00 Difficulty: Hard Goal: 1
Use the following to answer
questions 55-59:
A study by a bank compared the
average savings of customers who were depositors for three years or less, with
those who had been depositors for more than three years. The results of a sample are:
56. Assuming
that the financial officer wants to show that there is a difference in the
average savings balance between the two classes of depositors, what is the null
hypothesis? _____________________
Answer:
Difficulty:Medium Goal: 2
57. Fora = 0.05, what is the critical value of t? ___________
Answer:
2.069 Difficulty: Hard Goal: 1
58. What
is the computed test statistic? ______________
Answer:1.000 Difficulty: Hard Goal: 1
59. What
is the p-value if
= .05 and the test statistic is 2.807? _____
Answer:approximately 0.01
Difficulty: Hard Goal: 1
Multiple Choice
Use the following to
answer questions 60-66:
Accounting
procedures allow a business to evaluate their inventory at LIFO (Last In First
Out) or FIFO (First In First Out). A
manufacturer evaluated its finished goods inventory (in $ thousands) for five
products both ways. Based on the
following results, is LIFO more effective in keeping the value of his inventory
lower?
60. What is the null hypothesis?
A) 
.
B) 
.
C) 
.
D) 
.
Answer:C Difficulty: Medium Goal: 3
61. What
is the alternate hypothesis?
A) .
B) .
C) .
D) .
Answer:D Difficulty: Medium Goal: 3
62. What
is the degree of freedom?
A) 4
B) 5
C) 15
D) 10
E) 9
Answer:A Difficulty: Medium Goal: 3
63. If
you use the 5% level of significance, what is the critical t value?
A) +2.132
B) 2.776
C) +2.262
D) 2.228
Answer:A Difficulty: Medium Goal: 3
64. What
is the value of calculated t?
A) +1.93
B) 2.776
C) +0.0.47
D) –2.028
Answer:A Difficulty: Hard Goal: 3
65. What
is the decision at the 5% level of significance?
A) Fail to reject the null hypothesis and
conclude LIFO is more effective.
B) Reject the null hypothesis and conclude LIFO
is more effective.
C) Reject the alternate hypothesis and conclude
LIFO is more effective.
D) Fail to reject the null hypothesis and
conclude LIFO is not more effective.
Answer:D Difficulty: Hard Goal: 3
66. This example is what type of test?
A) One sample test of means.
B) Two sample test of means.
C) Paired t-test.
D) Test of proportions.
Answer:C Difficulty: Medium Goal: 3
Fill-in-the-Blank
Use the following to
answer questions 67-75:
To compare the
effect of weather on sales of soft drinks, a soda manufacturer sampled two
regions of the country with the following results. Is there a difference in sales between the 2
regions?
67. What
is the null hypothesis? _____________________
Answer:
Difficulty:Medium Goal: 2
68. What
is the alternate hypothesis? _______________________
Answer:
Difficulty:Medium Goal: 2
69. What
is the proportion of sales made in Market Area 1? ______
Answer:0.40
Difficulty: Easy Goal: 2
70. What is the proportion of sales made in Market
Area 2? ______
Answer:0.33
Difficulty: Easy Goal: 2
71. What
is the pooled estimate of the population proportion? _______
Answer:0.36
Difficulty: Hard Goal: 2
72. Using
the 1% level of significance, what is the critical value? _____
Answer:2.58 Difficulty: Medium Goal: 2
73. What
is the z-statistic? _____________
Answer:3.57
Difficulty: Hard Goal: 2
74. What is your decision? ____________________
Answer:reject
Difficulty: Medium Goal: 2
75. What
is your decision ifa = 0.01
and the z-statistic is –1.96? ____________________
Answer:fail to reject Difficulty: Medium Goal: 2
Use the following to
answer questions 76-79:
A financial planner
wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of
a sample of 35 income and 40 growth funds.
The mean increase for a two-year period for the income funds is $900. For the growth funds the mean increase is
$875. Income funds have a population
standard deviation of $35; growth funds have a population standard deviation of
$45. At the 0.05 significance level, is
there a difference in the mean yields of the two funds?
76. What
is the null hypothesis? __________________
Answer:
Difficulty:Easy
Goal: 1
77. What
is the computed value of the test statistic? ______________
Answer:2.70
Difficulty: Medium Goal: 1
78. What
is the p-value for the computed test statistic? ____________
Answer:0.007
Difficulty: Medium Goal: 1
79. What
decision is made about the null hypothesis using and ? = 0.05? ____________
Answer:Reject the null hypothesis. Difficulty: Medium Goal: 1
Essay
80. For hypotheses that compare two population
means, when is a pooled variance used?
Answer: Independent
populations and the population standard deviations are unknown and assumed to
be equal. Difficulty: Medium Goal: 1
81. For hypotheses that compare two population
means, when are the degrees of freedom adjusted?
Answer: Independent
populations, and the population standard deviations are unknown and assumed
unequal. Difficulty: Medium Goal: 1Chapter 11
Two Samples Tests of
Hypothesis
True/False
1. If the null hypothesis states that there is
no difference between the mean income of males and the mean income of females,
then the test is one-tailed.
Answer:False
Difficulty: Easy Goal: 1
AACSB: MD
2. If the null hypothesis states that there is
no difference between the mean net income retail stores in Chicago and New York
City, then the test is two-tailed.
Answer:True
Difficulty: Easy Goal: 1
3. If we are testing for the difference between
two population means, it is assumed that the sample observations from one
population are independent of the sample observations from the other
population.
Answer:True
Difficulty: Easy Goal: 1
4. If we are testing for the difference between
two population proportions, it is assumed that the two populations are
approximately normal and have equal variances.
Answer:False
Difficulty: Easy Goal: 2
5. If we are testing for the difference between
two population proportions, it is assumed that the two samples are large enough
that the binomial distribution can be approximated by the normal distribution.
Answer:True
Difficulty: Easy Goal: 2
AACSB: AS
6. When sample sizes are less than 30, a test
for the differences between two population means has n–1 degrees of
freedom.
Answer:False
Difficulty: Easy Goal: 1
7. If we are testing for the difference between
two population means and assume that the two populations have equal but unknown
standard deviations, then the test has (n1 + n2 – 2) degrees of freedom.
Answer:True Difficulty: Easy Goal: 1
AACSB: AS
8. If we are testing for the difference between
two population means and assume that the two populations have equal but unknown
standard deviations, the variances are pooled to compute the best estimated
variance.
Answer:True Difficulty: Easy Goal: 1
9. If we are testing for the difference between
two population means and assume that the two populations have unequal and
unknown standard deviations, the degrees of freedom for the test statistic must
be computed or calculated.
Answer:True Difficulty: Easy Goal: 1
10. If we are testing for the difference between
two population means and assume that the two populations have unequal and
unknown standard deviations, the variances are pooled to compute the best
estimated variance.
Answer:False Difficulty: Easy Goal: 1
AACSB: REF
11. If samples taken from two populations are not
independent, then a test of paired differences is applied.
Answer:True
Difficulty: Easy Goal: 3
12. The paired difference test has (n1 + n2 – 2) degrees of freedom.
Answer:False
Difficulty: Easy Goal: 3
13. When testing for the difference between two
dependent samples, n1 = n2.
Answer:True
Difficulty: Easy Goal: 3
14. We use the pooled estimate of the proportion
in testing the difference between two population proportions.
Answer:True
Difficulty: Medium Goal: 2
15. The pooled estimate of the proportion is
found by dividing the total number of samples by the total number of successes.
Answer:False
Difficulty: Medium Goal: 2
