File: ch16, Chapter 16: Analysis of Categorical Data
True/False
1. The chisquare distribution is continuous and has a range between minus infinity and plus infinity.
Ans: False
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
2. Chisquare goodnessoffit tests are always onetailed tests.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Easy
3. A chisquare goodnessoffit test can be used as an alternative to ztest for population proportions if there are only two classifications.
Ans: True
Response: See section 16.1 ChiSquare GoodnessofFit Test
Difficulty: Hard
4. A chisquare 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: ChiSquare 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: ChiSquare Test of Independence Difficulty: Hard
6. Chisquare test of independence is not useful for analyzing nominal data.
Ans: False
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence
Difficulty: Easy
7. Frequencies of responses to a questionnaire with two questions may be tallied nicely into a twoway table called a contingency table.
Ans: True
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence Difficulty: Easy
8. In chisquare test, if there are 8 rows and 4 columns, the number of degrees of freedom for the chisquare statistic would be 32.
Ans: False
Response: See section 16.2 Contingency Analysis: ChiSquare Test of Independence Difficulty: Medium
Multiple Choice
9. The number of degrees of freedom in a chisquare goodnessoffit 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 ChiSquare GoodnessofFit Test
Difficulty: Medium
10. The number of degrees of freedom in a chisquare goodnessoffit 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 ChiSquare GoodnessofFit Test
Difficulty: Medium
11. A business analyst wants to use the chisquare goodnessoffit 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 ChiSquare GoodnessofFit Test
Difficulty: Medium
12. A business analyst wants to use the chisquare goodnessoffit 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 ChiSquare GoodnessofFit Test
Difficulty: Medium
13. A business analyst wants to use the chisquare goodnessoffit 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 ChiSquare GoodnessofFit Test
Difficulty: Medium
14. A business analyst wants to use the chisquare goodnessoffit 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 chisquare 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 ChiSquare GoodnessofFit Test
Difficulty: Hard
15. A business analyst wants to use the chisquare goodnessoffit 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 chisquare 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 ChiSquare GoodnessofFit Test
Difficulty: Medium
16. A business analyst wants to use the chisquare goodnessoffit 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 ChiSquare GoodnessofFit Test
Difficulty: Medium
17. In a chisquare test of independence, the null hypothesis is ______________.
a) the two variables are independent
b) the two variables are not independent
c) the chisquares 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: ChiSquare Test of Independence
Difficulty: Medium
18. A chisquare 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 chisquare 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: ChiSquare Test of Independence
Difficulty: Medium 