19. Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether
the two population locations differ.
Sample 1:
17
20
18
25
16
22
Sample 2:
17
25
33
38
15
26
21
:
0
H
:
1
H
20. Use the 5% significance level to test the hypotheses
:
0
H
The two population locations are the same
:
1
H
The location of population A is to the right of the location of population B,
given that the data below are drawn from two independent samples:
Sample A:
9
11
9
10
12
8
5
Sample B:
8
7
5
7
9
5
6
8
21. If in a matched pairs experiment we find 25 negative, 5 zero, and 16 positive differences, perform the
sign test at the 5% significance level to determine whether the two population locations differ.
:
0
H
:
1
H
:
0
H
22. Apply the Kruskal–Wallis test to determine whether there is enough evidence at the 5% significance
level to infer that at least two of the populations represented by the samples below differ.
Sample
1
2
3
23
28
20
22
27
22
25
27
19
20
19
21
18
20
20
23. The data below are drawn from four independent samples.
Sample
1
2
3
4
13
15
18
9
9
10
15
10
16
15
17
6
12
14
18
6
15
13
8
Test at the 1% significance level to determine whether the population locations differ.
24. The following statistics are drawn from two independent samples:
800=
A
T
,
25=
A
n
,
1100=
B
T
,
28=
B
n
.
Test at the 5% significance level to determine whether the two population locations differ.
25. Use the following statistics to determine whether there is enough statistical evidence at the 1%
significance level to infer that the population locations differ.
T1 = 90, n1 = 6, T2 = 56, n2 = 6, T3 = 25, n3 = 6.
26. Apply the Friedman test to the following table of ordinal data to determine whether we can infer at the
10% significance level that at least two population locations differ.
Treatment
Block
1
2
3
4
1
2
5
3
1
2
1
4
5
4
3
3
4
2
2
4
2
5
4
1
5
1
5
3
5
27. In a diet test, each of four diet programs is applies to a sample of people. At the end of three weeks, the
amount of pounds people lost is shown below.
Diet Program
1
2
3
4
12
19
16
28
6
10
20
17
18
13
26
22
23
20
19
16
25
20
Test to determine whether there is enough evidence at the 5% significance level to infer that at least
two population locations differ.
28. Ten business people who fly frequently from Melbourne to Sydney were asked to rank four airlines in
terms of the quality of service. The people assigned scores using a 5-point Likert scale where: 1 = bad,
2 = poor, 3 = average, 4 = good, and 5 = excellent. The results are shown below.
Airline
Person
A
B
C
D
1
5
5
2
1
2
3
3
4
2
3
2
3
4
3
4
1
1
4
3
5
4
1
5
3
6
2
3
4
2
7
1
3
5
2
8
3
3
5
1
9
1
3
5
2
10
2
4
3
1
Which test is appropriate if you want to compare the quality of service of the four airlines?
29. Ten business people who fly frequently from Melbourne to Sydney were asked to rank four airlines in
terms of the quality of service. The people assigned scores using a 5-point Likert scale where: 1 = bad,
2 = poor, 3 = average, 4 = good, and 5 = excellent. The results are shown below.
Airline
Person
A
B
C
D
1
5
5
2
1
2
3
3
4
2
3
2
3
4
3
4
1
1
4
3
5
4
1
5
3
6
2
3
4
2
7
1
3
5
2
8
3
3
5
1
9
1
3
5
2
10
2
4
3
1
Can we conclude at the 5% significance level that there are differences in service quality among the
four airlines?
30. Ten business people who fly frequently from Melbourne to Sydney were asked to rank four airlines in
terms of the quality of service. The people assigned scores using a 5-point Likert scale where: 1 = bad,
2 = poor, 3 = average, 4 = good, and 5 = excellent. The results are shown below.
Airline
Person
A
B
C
D
1
5
5
2
1
2
3
3
4
2
3
2
3
4
3
4
1
1
4
3
5
4
1
5
3
6
2
3
4
2
7
1
3
5
2
8
3
3
5
1
9
1
3
5
2
10
2
4
3
1
Using the appropriate statistical table, what statement can be made about the p-value for the test?
31. Ten business people who fly frequently from Melbourne to Sydney were asked to rank four airlines in
terms of the quality of service. The people assigned scores using a 5-point Likert scale where: 1 = bad,
2 = poor, 3 = average, 4 = good, and 5 = excellent. The results are shown below.
Airline
Person
A
B
C
D
1
5
5
2
1
2
3
3
4
2
3
2
3
4
3
4
1
1
4
3
5
4
1
5
3
6
2
3
4
2
7
1
3
5
2
8
3
3
5
1
9
1
3
5
2
10
2
4
3
1
Use Excel to find the exact p–value for this test.
32. The marketing manager of a pizza chain is in the process of examining some of the demographic
characteristics of her customers. In particular, she would like to investigate the belief that the ages of
the customers of pizza parlours, hamburger emporiums and fast-food chicken restaurants are different.
As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below.
From previous analysis we know that the ages are not normally distributed.
Customer Age
Pizza
Hamburger
Chicken
23
26
25
19
20
28
25
18
36
17
35
23
36
33
39
25
25
27
28
19
38
31
17
31
Do these data provide enough evidence at the 10% significance level to infer that there are differences
in age among the customers of the three restaurants?
33. The marketing manager of a pizza chain is in the process of examining some of the demographic
characteristics of her customers. In particular, she would like to investigate the belief that the ages of
the customers of pizza parlours, hamburger emporiums and fast-food chicken restaurants are different.
As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below.
From previous analysis we know that the ages are not normally distributed.
Customer Age
Pizza
Hamburger
Chicken
23
26
25
19
20
28
25
18
36
17
35
23
36
33
39
25
25
27
28
19
38
31
17
31
Using the appropriate statistical table, what statement can be made about the p-value for the test?
34. The marketing manager of a pizza chain is in the process of examining some of the demographic
characteristics of her customers. In particular, she would like to investigate the belief that the ages of
the customers of pizza parlours, hamburger emporiums and fast-food chicken restaurants are different.
As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below.
From previous analysis we know that the ages are not normally distributed.
Customer Age
Pizza
Hamburger
Chicken
23
26
25
19
20
28
25
18
36
17
35
23
36
33
39
25
25
27
28
19
38
31
17
31
Use Excel to find the exact p–value for this test of whether there are differences in age among the
customers of the three restaurants.
35. The restaurant critic on a newspaper claims that the hamburgers one gets at the hamburger chain
restaurants are all equally bad, and that people who claim to like one hamburger over others are
victims of advertising. In fact, he claims that if there were no differences in appearance, then all
hamburgers would be rated equally. To test the critic’s assertion, ten teenagers are asked to taste
hamburgers from three different fast-food chains. Each hamburger is dressed in the same way
(mustard, relish, tomato and pickle) with the same type of bun. The teenagers taste each hamburger
and rate it on a 9-point scale with 1 = bad and 9 = excellent. The data are listed below.
Hamburger Ratings
Teenager
Chain 1
Chain 2
Chain 3
1
7
5
6
2
5
3
4
3
6
4
5
4
9
8
8
5
4
3
2
6
4
5
4
7
6
5
5
8
5
4
5
9
8
7
9
10
9
8
7
Can we infer at the 1% significance level that the critic is wrong?
36. The restaurant critic on a newspaper claims that the hamburgers one gets at the hamburger chain
restaurants are all equally bad, and that people who claim to like one hamburger over others are
victims of advertising. In fact, he claims that if there were no differences in appearance, then all
hamburgers would be rated equally. To test the critic’s assertion, ten teenagers are asked to taste
hamburgers from three different fast-food chains. Each hamburger is dressed in the same way
(mustard, relish, tomato and pickle) with the same type of bun. The teenagers taste each hamburger
and rate it on a 9-point scale with 1 = bad and 9 = excellent. The data are listed below.
Hamburger Ratings
Teenager
Chain 1
Chain 2
Chain 3
1
7
5
6
2
5
3
4
3
6
4
5
4
9
8
8
5
4
3
2
6
4
5
4
7
6
5
5
8
5
4
5
9
8
7
9
10
9
8
7
Using the appropriate statistical table, what statement can be made about the p-value for this test?
37. The restaurant critic on a newspaper claims that the hamburgers one gets at the hamburger chain
restaurants are all equally bad, and that people who claim to like one hamburger over others are
victims of advertising. In fact, he claims that if there were no differences in appearance, then all
hamburgers would be rated equally. To test the critic’s assertion, ten teenagers are asked to taste
hamburgers from three different fast-food chains. Each hamburger is dressed in the same way
(mustard, relish, tomato and pickle) with the same type of bun. The teenagers taste each hamburger
and rate it on a 9-point scale with 1 = bad and 9 = excellent. The data are listed below.
Hamburger Ratings
Teenager
Chain 1
Chain 2
Chain 3
1
7
5
6
2
5
3
4
3
6
4
5
4
9
8
8
5
4
3
2
6
4
5
4
7
6
5
5
8
5
4
5
9
8
7
9
10
9
8
7
Use Excel to find the exact p–value for this test.
38. Ten secretaries were selected at random from among the secretaries of a large university. The typing
speed (number of words per minute) was recorded for each secretary on two different brands of
computer keyboards. The following results were obtained.
Computer Keyboard
Secretary
Brand A
Brand B
Amy
75
74
Betty
85
86
Carol
73
72
Donna
79
70
Ellen
91
85
Faith
80
73
Gwen
83
72
Heather
74
65
Ingrid
81
79
Jody
70
64
Assume that the typing speeds are not normally distributed.
Perform the sign test to determine whether these data provide enough evidence at the 5% significance
level to infer that the brands differ with respect to typing speed.
39. Ten secretaries were selected at random from among the secretaries of a large university. The typing
speed (number of words per minute) was recorded for each secretary on two different brands of
computer keyboards. The following results were obtained.
Computer Keyboard
Secretary
Brand A
Brand B
Amy
75
74
Betty
85
86
Carol
73
72
Donna
79
70
Ellen
91
85
Faith
80
73
Gwen
83
72
Heather
74
65
Ingrid
81
79
Jody
70
64
Assume that the typing speeds are not normally distributed.
Perform the Wilcoxon signed rank sum test at the 5% significance level.
40. In a Kruskal–Wallis test, the following statistics were obtained:
T1 = 55, n1 = 5, T2 = 54, n2 = 5, T3 = 54, n3 = 5, T4 = 47, n4 = 5.
Conduct the test at the 5% significance level.
41. In a Kruskal–Wallis test, the following statistics were obtained:
T1 = 55, n1 = 5, T2 = 54, n2 = 5, T3 = 54, n3 = 5, T4 = 47, n4 = 5.
What is the most accurate statement that can be made about the p-value of this test?
42. In a Kruskal–Wallis test, the following statistics were obtained:
T1 = 55, n1 = 5, T2 = 54, n2 = 5, T3 = 54, n3 = 5, T4 = 47, n4 = 5.
Use Excel to find the exact p–value for this test.
43. The general manager of a frozen TV dinner maker must decide which one of four new dinners to
introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is
sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent.
The results are shown below.
Taste Ratings
Respondent
Dinner 1
Dinner 2
Dinner 3
Dinner 4
1
6
6
4
5
2
5
5
2
4
3
7
7
3
4
4
6
6
5
4
5
7
6
4
3
6
7
5
3
5
7
6
4
3
4
8
5
6
4
6
9
4
4
3
5
10
7
5
6
4
Which test can the general manager use to help him make a decision?
44. The general manager of a frozen TV dinner maker must decide which one of four new dinners to
introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is
sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent.
The results are shown below.
Taste Ratings
Respondent
Dinner 1
Dinner 2
Dinner 3
Dinner 4
1
6
6
4
5
2
5
5
2
4
3
7
7
3
4
4
6
6
5
4
5
7
6
4
3
6
7
5
3
5
7
6
4
3
4
8
5
6
4
6
9
4
4
3
5
10
7
5
6
4
Can the general manager infer at the 5% significance level that there are differences in the taste ratings
of the four dinners?
45. The general manager of a frozen TV dinner maker must decide which one of four new dinners to
introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is
sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent.
The results are shown below.
Taste Ratings
Respondent
Dinner 1
Dinner 2
Dinner 3
Dinner 4
1
6
6
4
5
2
5
5
2
4
3
7
7
3
4
4
6
6
5
4
5
7
6
4
3
6
7
5
3
5
7
6
4
3
4
8
5
6
4
6
9
4
4
3
5
10
7
5
6
4
Using the appropriate statistical table, what statement can be made about the p-value for the test?
46. The general manager of a frozen TV dinner maker must decide which one of four new dinners to
introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is
sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent.
The results are shown below.
Taste Ratings
Respondent
Dinner 1
Dinner 2
Dinner 3
Dinner 4
1
6
6
4
5
2
5
5
2
4
3
7
7
3
4
4
6
6
5
4
5
7
6
4
3
6
7
5
3
5
7
6
4
3
4
8
5
6
4
6
9
4
4
3
5
10
7
5
6
4
Use Excel to find the exact p–value for this test.
47. A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a
movie differently. With this objective, he commissioned a survey that asked people their ratings of
their most recently watched movies. The rating categories were:
1 = terrible.
2 = fair.
3 = good.
4 = excellent.
Each respondent was also asked to categorise his or her age as either:
1 = teenager.
2 = young adult (20–34).
3 = middle age (35–50).
4 = senior (over 50).
The results are shown below.
Movie Ratings
Teenager
Young Adult
Middle Age
Senior
3
2
3
3
4
3
2
4
3
3
1
4
3
2
2
3
3
2
2
3
4
1
3
4
2
3
1
4
4
2
4
3
Which test the movie critic can use in this situation?
48. A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a
movie differently. With this objective, he commissioned a survey that asked people their ratings of
their most recently watched movies. The rating categories were:
1 = terrible.
2 = fair.
3 = good.
4 = excellent.
Each respondent was also asked to categorise his or her age as either:
1 = teenager.
2 = young adult (20–34).
3 = middle age (35–50).
4 = senior (over 50).
The results are shown below.
Movie Ratings
Teenager
Young Adult
Middle Age
Senior
3
2
3
3
4
3
2
4
3
3
1
4
3
2
2
3
3
2
2
3
4
1
3
4
2
3
1
4
4
2
4
3
Do these data provide sufficient evidence to infer at the 5% significance level that there were
differences in ratings among the different age categories?
49. A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a
movie differently. With this objective, he commissioned a survey that asked people their ratings of
their most recently watched movies. The rating categories were:
1 = terrible.
2 = fair.
3 = good.
4 = excellent.
Each respondent was also asked to categorise his or her age as either:
1 = teenager.
2 = young adult (20–34).
3 = middle age (35–50).
4 = senior (over 50).
The results are shown below.
Movie Ratings
Teenager
Young Adult
Middle Age
Senior
3
2
3
3
4
3
2
4
3
3
1
4
3
2
2
3
3
2
2
3
4
1
3
4
2
3
1
4
4
2
4
3
Using the appropriate statistical table, what statement can be made about the p-value for the test?
50. A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a
movie differently. With this objective, he commissioned a survey that asked people their ratings of
their most recently watched movies. The rating categories were:
1 = terrible.
2 = fair.
3 = good.
4 = excellent.
Each respondent was also asked to categorise his or her age as either:
1 = teenager.
2 = young adult (20–34).
3 = middle age (35–50).
4 = senior (over 50).
The results are shown below.
Movie Ratings
Teenager
Young Adult
Middle Age
Senior
3
2
3
3
4
3
2
4
3
3
1
4
3
2
2
3
3
2
2
3
4
1
3
4
2
3
1
4
4
2
4
3
Use Excel to find the exact p–value for this test.
51. Because of the cost of producing television shows and the profits associated with successful shows,
television network executives are keenly interested in public opinion. A network has recently
developed three comedy series. The pilot of each series is shown to 10 randomly selected people, who
evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent. The results are shown
below.
Assessments of Television Shows
Person
Show 1
Show 2
Show 3
1
6
4
7
2
5
4
5
3
7
6
8
4
7
7
8
5
9
9
9
6
5
7
6
7
4
4
5
8
6
3
7
9
5
6
6
10
7
7
8
Can we infer at the 5% significance level that differences exist among the show’s evaluations?
52. Because of the cost of producing television shows and the profits associated with successful shows,
television network executives are keenly interested in public opinion. A network has recently
developed three comedy series. The pilot of each series is shown to 10 randomly selected people, who
evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent. The results are shown
below.
Assessments of Television Shows
Person
Show 1
Show 2
Show 3
1
6
4
7
2
5
4
5
3
7
6
8
4
7
7
8
5
9
9
9
6
5
7
6
7
4
4
5
8
6
3
7
9
5
6
6
10
7
7
8
Using the appropriate statistical table, what statement can be made about the p-value for this test?
53. Because of the cost of producing television shows and the profits associated with successful shows,
television network executives are keenly interested in public opinion. A network has recently
developed three comedy series. The pilot of each series is shown to 10 randomly selected people, who
evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent. The results are shown
below.
Assessments of Television Shows
Person
Show 1
Show 2
Show 3
1
6
4
7
2
5
4
5
3
7
6
8
4
7
7
8
5
9
9
9
6
5
7
6
7
4
4
5
8
6
3
7
9
5
6
6
10
7
7
8
Use Excel to find the exact p–value for this test.
54. In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly
reviewed by university lecturers. Suppose that Cengage Australia publishing company has recently
received two manuscripts for statistics books. To help them decide which one to publish, both are sent
to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10
lecturers rate manuscript 1 as better and 20 rate manuscript 2 as better.
Which test is appropriate for this situation?
55. In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly
reviewed by university lecturers. Suppose that Cengage Australia publishing company has recently
received two manuscripts for statistics books. To help them decide which one to publish, both are sent
to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10
lecturers rate manuscript 1 as better and 20 rate manuscript 2 as better.
Can Cengage Australia conclude at the 5% significance level that manuscript 2 is more highly rated
than manuscript 1?
56. In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly
reviewed by university lecturers. Suppose that Cengage Australia publishing company has recently
received two manuscripts for statistics books. To help them decide which one to publish, both are sent
to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10
lecturers rate manuscript 1 as better and 20 rate manuscript 2 as better.
What is the p-value of this test?
57. A supermarket chain has its own house brand of ice cream. The general manager claims that her ice
cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40
individuals are randomly selected to participate in the following experiment. Each respondent is given
the two brands of ice cream to taste (without any identification) and asked to judge which one is better.
Suppose that 25 people judge the ice cream parlour brand better, four say that the brands taste the
same, and the rest claim that the supermarket brand is better.
Which test is appropriate for this situation?
58. A supermarket chain has its own house brand of ice cream. The general manager claims that her ice
cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40
individuals are randomly selected to participate in the following experiment. Each respondent is given
the two brands of ice cream to taste (without any identification) and asked to judge which one is better.
Suppose that 25 people judge the ice cream parlour brand better, four say that the brands taste the
same, and the rest claim that the supermarket brand is better.
Can we conclude at the 1% significance level that the general managers’ claim is false?
59. A supermarket chain has its own house brand of ice cream. The general manager claims that her ice
cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40
individuals are randomly selected to participate in the following experiment. Each respondent is given
the two brands of ice cream to taste (without any identification) and asked to judge which one is better.
Suppose that 25 people judge the ice cream parlour brand better, four say that the brands taste the
same, and the rest claim that the supermarket brand is better.
What is the p-value of this test?