b.
The number of degrees of freedom in a test of a contingency table with r rows and c
columns is (r − 1)(c − 1).
c.
The number of degrees of freedom in a goodness-of-fit test with k categories is k − 1.
d.
All of these choices are true.
94. Suppose that two shipping companies, A and B, each decide to estimate the annual percentage of
shipments on which a $100 or greater claim for loss or damage was filed by sampling their records,
and they report the data shown below.
Company A
Company B
Total shipments sampled
800
600
Number of shipments with a claim $100
200
100
The owner of Company B is hoping to use these data to show that her company is superior to
Company A with regard to the percentage of claims filed. Which test would be used to properly
analyze the data in this experiment?
a.
The
2 test of a contingency table in a two-way contingency table.
b.
The
2 goodness-of-fitness test.
c.
The z-test for the difference in two proportions.
d.
The ANOVA F test for main treatment effect.
95. Which of the following tests is used to analyze nominal data?
a.
The z-test for one proportion, p, or difference of two proportions, p1 − p2.
b.
The chi-squared goodness-of-fitness test.
c.
The chi-squared test of a contingency table.
d.
All of these choices are true.
96. Which of the following tests is appropriate for nominal data if the problem objective is to compare two
or more populations and the number of categories is at least 2?
a.
The z-test for one proportion, p, or difference of two proportions, p1 − p2.
b.
The chi-squared goodness-of-fitness test.
c.
The chi-squared test of a contingency table.
d.
All of these choices are true.
97. Which of the following tests is appropriate for nominal data if the problem objective is to describe a
population with more than two categories?
a.
z-test for one proportion, p, or difference of two proportions, p1 − p2.
b.
chi-squared goodness-of-fitness test.
c.
chi-squared test of a contingency table.
d.
All of these choices are true.
98. Which of the following tests is appropriate for nominal data if the problem objective is to compare two
populations and there are exactly 2 categories?
a.
The z-test for the difference of two proportions, p1 − p2.
b.
The chi-squared test of a contingency table.
c.
Both a and b.
d.
None of these choices.
99. There are two critical factors in identifying the technique used when the data are nominal. The first is
the problem objective. The second is the number of ____________________ that nominal variable can
assume.
100. If you want to describe a population with two categories, you can use a(n) ____________________
test of p or the chi-squared goodness-of-fit test.
z–
101. If you want to describe a population with more than two categories, you can use a chi-squared
____________________ test.
102. If you want to compare two populations that each have two categories, you can use a z-test for two
proportions, or a chi-squared test of a(n) ____________________.
103. If you want to compare two populations that each have more than two categories, you can use a
chi-squared test of a(n) ____________________.
104. For comparing two or more populations each having two or more categories, use a(n)
____________________ test of a(n) ____________________.
105. To analyze the relationship between two nominal variables, use a(n) ____________________ test of
a(n) ____________________.
106. If we square the value of z (the test statistic in the test of a proportion) we produce the
____________________ statistic.
107. What are the two critical factors in identifying the technique used when the data are nominal?
108. Which test(s) can you use when you want to describe a population with two categories?
109. If you want to describe a population with more than two categories, which test(s) can you use?
110. If you want to compare two populations that each have two categories, which test(s) can you use?
111. If you want to compare two populations that each have more than two categories, which test(s) can
you use?
112. For comparing two or more populations each having two or more categories, you can use which
test(s)?
113. To analyze the relationship between two nominal variables, which test(s) can you use?
114. What statistic do we get when we square the value of z?
115. The null hypothesis states that the sample data came from a normally distributed population. The
researcher calculates the sample mean and the sample standard deviation from the data. The data
arrangement consisted of five categories. Using
= .05, the appropriate critical value for this
chi-squared test for normality is 5.99147.
116. The number of degrees of freedom associated with the chi-squared test for normality is the number of
intervals used minus the number of parameters estimated from the data.
117. In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed
population. The researcher estimated the population mean and population standard deviation from a
sample of 300 observations. In addition, the researcher used 6 standardized intervals to test for
normality. Using a 2.5% level of significance, the critical value for this test is 14.4494.
118. In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed
population. The researcher estimated the population mean and population standard deviation from a
sample of 200 observations. In addition, the researcher used 5 standardized intervals to test for
normality. Using a 10% level of significance, the critical value for this test is 4.60517.
119. The number of degrees of freedom in testing for normality is the:
a.
number of intervals used to test the hypothesis minus one.
b.
number of parameters estimated minus one.
c.
number of intervals used to test the hypothesis minus one minus the number of parameters
estimated.
d.
None of these choices.
120. The number of degrees of freedom in a chi-squared test for normality, where the number of
standardized intervals is 5 and there are 2 population parameters to be estimated from the data, is equal
to:
a.
5
b.
4
c.
3
d.
2
121. In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed
population. The researcher estimated the population mean and population standard deviation from a
sample of 500 observations. In addition, the researcher used 6 standardized intervals to test for
normality. Using a 5% level of significance, the critical value for this test is:
a.
11.1433
b.
9.3484
c.
7.8147
d.
9.4877
122. We can use the goodness-of-fit test to determine whether data were drawn from any distribution of
interest. The most common application of this procedure is a test of ____________________.
123. To test for normality, the ____________________ hypothesis specifies probabilities of certain
intervals within the normal distribution.
124. To test for normality, the ____________________ hypothesis is that at least two proportions differ
from their specified values.
125. The number of degrees of freedom associated with the chi-squared test statistic for normality is the
number of ____________________ minus 1 minus the number of ____________________ estimated.
126. A large value of the chi-squared test statistic in a test of normality means you reject H0 and conclude
that the data ____________________ (do/do not) come from a normal distribution.
127. The chi-squared test for normality must follow the rule of ____________________ regarding expected
values.
128. The following data are believed to have come from a normal probability distribution.
26
21
25
20
21
29
26
23
22
24
24
30
23
32
26
24
32
16
36
26
21
31
26
23
32
35
40
30
14
26
46
27
33
25
27
21
26
18
29
36
The mean of this sample equals 26.80, and the standard deviation equals 6.378. Use the
goodness-of-fit test at the 5% significance level to test whether the data indeed come from a normal
distribution.
Z −1
−1 Z 0
0 Z 1
Z > 1
129. Suppose that a random sample of 60 observations was drawn from a population. After calculating the
mean and standard deviation, each observation was standardized and the number of observations in
each of the intervals below was counted. Can we infer at the 10% significance level that the data were
drawn from a normal population?
Intervals
Frequency
Z −1
8
−1 < Z 0
30
0 < Z 1
17
Z > 1
5
130. Suppose that a random sample of 150 observations was drawn from a population. After calculating the
mean and standard deviation, each observation was standardized and the number of observations in
each of the intervals below was counted. Can we infer at the 5% significance level that the data were
drawn from a normal population?
Intervals
Frequency
Z −1.5
15
−1.5 < Z −.5
32
−.5 Z .5
65
.5 < Z 1.5
25
Z > 1.5
13