# File: ch16, Chapter 16: Analysis of Categorical Data

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File: ch16, Chapter 16: Analysis of Categorical Data

True/False

1. The chi-square distribution is continuous and has a range between minus infinity and plus infinity.

Ans: False

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

2. Chi-square goodness-of-fit tests are always one-tailed tests.

Ans: True

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Easy

3. A chi-square goodness-of-fit test can be used as an alternative to z-test for population proportions if there are only two classifications.

Ans: True

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

4. A chi-square test of independence can be used to analyze the frequencies of two variables with multiple categories to check whether the two variables are independent.

Ans: True

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

5. If two variables are independent, the expected frequency of the intersection of two of their respective categories, say A and F, is always equal to the product of the frequencies of category A and category F divided by the total frequency.

Ans: True

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Hard

6. Chi-square test of independence is not useful for analyzing nominal data.

Ans: False

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Easy

7. Frequencies of responses to a questionnaire with two questions may be tallied nicely into a two-way table called a contingency table.

Ans: True

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Easy

8. In chi-square test, if there are 8 rows and 4 columns, the number of degrees of freedom for the chi-square statistic would be 32.

Ans: False

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence Difficulty: Medium

Multiple Choice

9. The number of degrees of freedom in a chi-square goodness-of-fit test in which the fit of a Poisson distribution to the observed frequencies in eight categories is being tested is equal to _________.

a) 5

b) 6

c) 7

d) 8

e) 9
Ans: b

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

10. The number of degrees of freedom in a chi-square goodness-of-fit test in which the fit of a normal distribution to the observed frequencies in eight categories is being tested is equal to _________.

a) 5

b) 6

c) 7

d) 8

e) 9
Ans: a

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

11. A business analyst wants to use the chi-square goodness-of-fit test if a uniform distribution is a good fit for the following observed frequencies in eight categories along a single dimension. The desired level of significance is 0.05.

 Category 1 2 3 4 5 6 7 8 Frequency 313 319 309 310 316 299 317 313

The number of degrees of freedom for this test is ___________.

a) 4

b) 5

c) 6

d) 7

e) 8
Ans: d

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

12. A business analyst wants to use the chi-square goodness-of-fit test if a uniform distribution is a good fit for the following observed frequencies in eight categories along a single dimension. The desired level of significance is 0.05.

 Category 1 2 3 4 5 6 7 8 Frequency 313 319 309 310 316 299 317 313

The expected frequency in Category 4 is ___________.

a) 412

b) 312

c) 612

d) 236

e) 328
Ans: b

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

13. A business analyst wants to use the chi-square goodness-of-fit test if a uniform distribution is a good fit for the following observed frequencies in eight categories along a single dimension. The desired level of significance is 0.05.

 Category 1 2 3 4 5 6 7 8 Frequency 313 319 309 310 316 299 317 313

The expected frequency in Category 6 is ___________.

a) 412

b) 312

c) 612

d) 236

e) 328
Ans: b

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

14. A business analyst wants to use the chi-square goodness-of-fit test if a uniform distribution is a good fit for the following observed frequencies in eight categories along a single dimension. The desired level of significance is 0.05.

 Category 1 2 3 4 5 6 7 8 Frequency 313 319 309 310 316 299 317 313

The observed chi-square value for this test is ___________.

a) 4.28

b) 3.16

c) 6.72

d) 0.26

e) 0.88
Ans: e

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Hard

15. A business analyst wants to use the chi-square goodness-of-fit test if a uniform distribution is a good fit for the following observed frequencies in eight categories along a single dimension. The desired level of significance is 0.05.

 Category 1 2 3 4 5 6 7 8 Frequency 313 319 309 310 316 299 317 313

The critical table value of the chi-square statistic for this test is ___________.

a) 18.12

b) 17.80

c) 14.07

d) 10.98

e) 10.84
Ans: c

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

16. A business analyst wants to use the chi-square goodness-of-fit test if a uniform distribution is a good fit for the following observed frequencies in eight categories along a single dimension. The desired level of significance is 0.05.

 Category 1 2 3 4 5 6 7 8 Frequency 313 319 309 310 316 299 317 313

The correct decision for the analyst is to ______________ ___________.

a) reject the null hypothesis that the observed distribution is uniform

b) reject the null hypothesis that the observed distribution is not uniform

c) fail to reject the null hypothesis that the observed distribution is uniform

d) fail to reject the null hypothesis that the observed distribution is not uniform

e) conclude that the test is inconclusive
Ans: c

Response: See section 16.1 Chi-Square Goodness-of-Fit Test

Difficulty: Medium

17. In a chi-square test of independence, the null hypothesis is ______________.

a) the two variables are independent

b) the two variables are not independent

c) the chi-squares of the two variables are equal

d) the means of the two variables are equal

e) the variances of the two variables are equal
Ans: a

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Medium

18. A chi-square test of independence is being used to determine if two variables are independent at a level of significance of 5%. One variable has 2 categories, and the other variable has 5 categories. The critical value of chi-square for this test is ___________.

a) 9.488

b) 11.143

c) 14.86

d) 11.07

e) 16.92
Ans: a

Response: See section 16.2 Contingency Analysis: Chi-Square Test of Independence

Difficulty: Medium