48. The null hypothesis in a chi-squared test of a contingency table is that the two nominal variables are
____________________.
49. The alternative hypothesis in a chi-squared test of a contingency table is that the two nominal variables
are ____________________.
50. You find the expected value for each cell in a chi-squared test for a contingency table by multiplying
the ____________________ total by the ____________________ total and dividing by the sample
size, n.
51. The expected values of a contingency table are calculated based on the assumption that H0 is
____________________.
52. The number of degrees of freedom associated with a chi-squared test of a contingency table is
____________________.
53. A large value of a chi-squared test statistic in a test of a contingency table leads you to conclude the
two variables are ____________________.
54. Before a chi-squared test of a contingency table can be carried out, the expected values of all cells
should be greater than or equal to ____________________.
55. A chi-squared test of a contingency table can be used to determine whether two nominal variables are
____________________.
56. A chi-squared test of a contingency table can be used to infer that differences exist between
____________________ populations of nominal variables.
57. Conduct a test to determine whether the two classifications A and B are independent, using the data in
the accompanying table and
= .05.
B1
B2
B3
A1
35
25
20
A2
25
20
25
58. The human resources manager of a consumer product company asked a random sample of employees
how they felt about the work they were doing. The following table gives a breakdown of their
responses by whether the employee is part time or full time (aka work status). Do the data provide
sufficient evidence to conclude that the level of job satisfaction is related to their work status? Use
=
.10.
Response
Gender
Very Interesting
Not Interesting
Full time
70
9
Part time
35
11
59. The owner of a consumer products company asked a random sample of employees how they felt about
the work they were doing. The following table gives a breakdown of their responses by age. Is there
sufficient evidence to conclude that the level of job satisfaction is related to age? Use
= .10.
Response
Age
Very Interesting
Fairly Interesting
Not Interesting
Under 30
31
24
13
Between 30 and 50
42
30
4
Over 50
32
21
3
60. A sports preference poll showed the following data for adults and children:
Favorite Sport
Gender
Baseball
Soccer
Rugby
Hockey
Archery
Adults
24
17
30
18
22
Children
21
20
22
12
28
Use the 5% level of significance and test to determine whether sports preferences depend on age
group.
61. A major insurance firm interviewed a random sample of 1,200 college students to find out the type of
life insurance preferred, if any. The results follow:
Insurance Preference
Gender
Term
Whole Life
No Insurance
Female
100
80
325
Male
160
60
475
Is there evidence that life insurance preference of male students is different than that of female
students? Test using the 5% level of significance.
62. The number of ATVs sold by three salespersons over a 3-month period is shown below:
Brand of ATV
Salesperson
Brand A
Brand B
Brand C
Juan
7
2
6
Pedro
11
4
8
Fernando
8
5
3
Use the 5% level of significance and test for the independence of salesperson and type of product sold.
63. The Chairman of a committee has recently circulated pamphlets among the members, attempting to
convince them that pension benefits should be the primary issue. A subsequent survey revealed the
following breakdown of the members according to the plant at which they worked and the issue that
they felt should be supported as the primary one.
Issues
Plant Location
Very Interesting
Not Interesting
New Mexico
60
78
Utah
70
74
Do the data indicate at the 5% significant level that there are differences between the two plants
regarding which issue should be the primary one?
Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or
not a child was present in the car. A sample of 1,000 people treated for injuries sustained from vehicle
accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2)
seat belt usage (worn or not worn) during the accident. The data are shown in the table below.
Child present in car
Seat Belts
NO
YES
Worn
83
200
Not Worn
337
380
64. {Seat Belts Narrative} Which test would be used to properly analyze the data in this experiment?
65. {Seat Belts Narrative} State the appropriate null and alternative hypotheses for this experiment.
66. {Seat Belts Narrative} Prepare the table of expected values.
67. {Seat Belts Narrative} Calculate the value of the test statistic.
68. {Seat Belts Narrative} How many degrees of freedom are associated with the proper test in this
experiment?
69. {Seat Belts Narrative} At 5% level of significance, what is the critical value of the test statistic?
70. {Seat Belts Narrative} At 5% level of significance, what is the proper conclusion?
71. If we want to test for differences between two populations of nominal data with exactly two categories,
we can employ either the z-test of p1 − p2, or the chi-squared test of a contingency table.
72. When the problem objective is to describe a population of nominal data with exactly two categories,
we can employ either the z-test of a population proportion p, or the chi-squared goodness-of-fit test.
73. If we want to perform a one-tail test of a population proportion p, we can employ either the z-test of p,
or the chi-squared goodness-of-fit test.
74. If we want to perform a two-tail test of a population proportion p, we can only use the z-test of p.
75. If we want to perform a two-tail test for differences between two populations of nominal data with
exactly two categories, we can employ either the z-test of p1 − p2, or the chi-squared test of a
contingency table.
76. If we want to perform a one-tail test for differences between two populations of nominal data with
exactly two categories, we must employ the z-test of p1 − p2.
77. When we describe a population of nominal data, with exactly two categories, the multinomial
experiment is actually a binomial experiment with one of the categorical outcomes labeled “success”
and the other labeled “failure“.
78. When we test for differences between two populations of nominal data with two categories, we can use
only one technique, namely, the chi-squared test of a contingency table.
79. Mathematical statisticians have established that if we square the value of z, the test statistic for the test
of one proportion p, we produce the
2 statistic. That is, z2 =
2.
80. To describe a population with more than two categories you can only use a chi-squared goodness-of-fit
test.
81. In testing the difference between two proportions using the normal distribution, we may use either a
one-tailed or two-tailed test.
82. A test for the differences between two proportions can be performed using the chi-squared distribution.
83. A test for whether one proportion is higher than the other can be performed using the chi-squared
distribution.
84. If we use the chi-squared method of analysis we must first check that there are at least 5 observations
in each cell of the contingency table.
85. The squared difference between the observed and expected frequencies should be large if there is a
significant difference between the proportions.
86. Which statistical technique is appropriate when we compare two or more populations of qualitative
data with two or more categories?
a.
The z-test of the difference between two proportions.
b.
The chi-squared test of a contingency table.
c.
The chi-squared goodness-of-fit test.
d.
Both a and b.
87. Which of the following tests is appropriate for nominal data if the problem objective is to compare two
populations and the number of categories exceeds 2?
a.
The z-test for one proportion, p, or difference of two proportions, p1 − p2.
b.
The chi-squared goodness-of-fit test.
c.
The chi-squared test of a contingency table.
d.
All of these choices are true.
88. If we want to conduct a one-tail test of a population proportion, we can employ:
a.
z-test of a population proportion.
b.
the chi-squared test of a binomial experiment since z2 =
2.
c.
the chi-squared test of a contingency table.
d.
Both a and b
89. If we want to conduct a two-tail test of a population proportion, we can employ:
a.
z-test of a population proportion.
b.
the chi-squared test of a binomial experiment since z2 =
2.
c.
the chi-squared test of a contingency table.
d.
Both a and b
90. Which statistical technique is appropriate when we describe a single population of qualitative data
with exactly two categories?
a.
The z-test of a population proportion.
b.
The chi-squared goodness-of-fit test.
c.
The chi-squared test of a contingency table.
d.
Both a and b.
91. The chi-squared distribution is used in:
a.
a goodness-of-fit test.
b.
a test of a contingency table.
c.
describing a population having more than two categories.
d.
All of these choices are true.
92. Which of the following tests does not use the chi-squared distribution?
a.
Test of a contingency table.
b.
Goodness-of-fit test.
c.
One tailed test for two proportions.
d.
None of these choices.
93. Which of the following statements is true for chi-squared tests?
a.
Testing for equal proportions is identical to testing for goodness-of-fit.