# File: Ch16, Chapter 16: Chi-Square Analysis

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File: Ch16, Chapter 16: Chi-Square Analysis

True/False

1. In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.

Ans: True

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

Difficulty: Easy

2. In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies.

Ans: False

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

Difficulty: Easy

3. The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated.

Ans: False

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

Difficulty: Easy

4. The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated minus one.

Ans: True

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

Difficulty: Easy

5. A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a normal distribution (the mean and the standard deviation of which must be estimated) for a data with "k" categories. This test has (k-3) degrees of freedom.

Ans: True

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

Difficulty: Medium

6. The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is the same as the expected distribution.

Ans: True

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

Difficulty: Medium

7. The decision rule in a chi-square goodness-of-fit test is to reject the null hypothesis if the computed chi-square is greater than the table chi-square.

Ans: True

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

Difficulty: Medium

8. When using the chi-square goodness-of-fit test, we must make sure that none of the expected frequencies is less than 30.

Ans: False

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

Difficulty: Medium

9. A chi-square goodness-of-fit test to determine if the observed frequencies in seven categories are uniformly distributed has six degrees of freedom.

Ans: True

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

Difficulty: Medium

10. A chi-square goodness-of-fit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom.

Ans: False

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

Difficulty: Medium

11. A two-way table used for a test of independence is sometimes called a contingency table.

Ans: True

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

Difficulty: Easy

12. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 12.

Ans: False

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

Difficulty: Easy

13. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 7.

Ans: False

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

Difficulty: Easy

14. In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 6.

Ans: True

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

Difficulty: Easy

15. The null hypothesis for a chi-square test of independence is that the two variables are not related.

Ans: True

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

Difficulty: Easy

Multiple Choice

16. A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C) more than the other two. A sample of 60 consumers is used. What is the expected frequency for category A?

a) 1/3

b) 20

c) 60

d) 10

e) 30
Ans: b

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

Difficulty: Easy

17. A goodness of fit test is to be performed to see if Web Surfers prefer any of four Web sites (A, B, C and D) more than the other three. A sample of 60 consumers is used. What is the expected frequency for Web site A?

a) 1/4

b) 20

c) 15

d) 10

e) 30
Ans: c

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

Difficulty: Easy

18. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the degrees of freedom for this test are _______.

a) 5

b) 4

c) 3

d) 2

e) 1
Ans: b

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

Difficulty: Medium

19. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the critical value of chi-square is _______.

a) 7.78

b) 15.09

c) 9.24

d) 13.28

e) 15.48
Ans: d

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

Difficulty: Medium

20. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the observed value of chi-square is _______.

a) 12.09

b) 9.82

c) 13.28

d) 17.81

e) 2.09
Ans: e

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

Difficulty: Middle

21. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using a = .01, the appropriate decision is _______.

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

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

c) do not reject the null hypothesis that the observed distribution is uniform

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

e) do nothing
Ans: c

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

Difficulty: Hard

22. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .01, the critical chi-square value is _______.

a) 13.277

b) 15.086

c) 7.779

d) 11.070

e) 14.356
Ans: a

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

Difficulty: Medium

23. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .01, the observed chi-square value is _______.

a) 1.18

b) 9.10

c) 20.27

d) 4.51

e) 19.70
Ans: b

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

Difficulty: Medium

24. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .01, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

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

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

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

e) do nothing
Ans: a

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

Difficulty: Hard

25. A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26. Using a = .10, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

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

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

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

e) do nothing
Ans: c

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

Difficulty: Hard

26. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .05, the critical chi square value is _______.

a) 13.277

b) 15.086

c) 7.8147

d) 11.070

e) 15.546
Ans: c

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

Difficulty: Easy

27. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .05, the observed chi-square value is _______.

a) 5.418

b) 9.10

c) 20.27

d) 4.51

e) 7.86
Ans: a

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

Difficulty: Medium

28. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .05, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

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

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

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

e) do nothing
Ans: a

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

Difficulty: Hard

29. A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .10, the appropriate decision is _______.

a) do not reject the null hypothesis that the observed distribution is uniform

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

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

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

e) do nothing
Ans: a

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

Difficulty: Hard

30. A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 6 categories, and lambda must be estimated. How many degrees of freedom should be used?

a) 6

b) 5

c) 4

d) 3

e) 2
Ans: c

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

Difficulty: Medium

31. A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and lambda must be estimated. How many degrees of freedom should be used?

a) 8

b) 7

c) 6

d) 5

e) 4

Ans: c

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

Difficulty: Medium

32. A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and lambda must be estimated. Alpha is chosen to be 0.10. The critical (table) value of chi-square is _______.

a) 10.645

b) 12.017

c) 3.828

d) 16.812

e) 17.345
Ans: a

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

Difficulty: Easy

33. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

 Category 0 1 2 3 4 5 Observed 47 56 39 22 18 10

Using a = 0.10, the critical chi-square value for this goodness-of-fit test is _______.

a) 1.064

b) 13.277

c) 9.236

d) 8.799

e) 7.779
Ans: e

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

Difficulty: Easy

34. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

 Category 0 1 2 3 4 5 Observed 47 56 39 22 18 10

Using a = 0.10, the observed chi-square value for this goodness-of-fit test is ____.

a) 2.28

b) 14.56

c) 17.43

d) 1.68

e) 2.67
Ans: b

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

Difficulty: Hard

35. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

 Category 0 1 2 3 4 >5 Observed 7 18 25 17 12 5

Using a = 0.10, the critical value of chi-square for the data is _______.

a) 9.236

b) 7.779

b) 1.064

c) 13.277

d) 12.89
Ans: b

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

Difficulty: Medium

36. A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected:

 Category 0 1 2 3 4 >5 Observed 7 18 25 17 12 5

Using a = 0.10, the value of the observed chi-square for the data is _______.

a) 19.37

b) 2.29

c) 1.74

d) 3.28

e) 4.48
Ans: c

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

Difficulty: Hard

37. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.

 Cars per 15 minute interval 0 1 2 3 4 >5 Observed Frequency 5 15 17 12 10 8

The number of degrees of freedom for this goodness-of-fit test is _______.

a) 5

b) 4

c) 3

d) 2

e) 1
Ans: b

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

Difficulty: Medium

38. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.

 Cars per 15 minute interval 0 1 2 3 4 >5 Observed Frequency 5 15 17 12 10 8

Using a = 0.05, the critical value of chi-square for this goodness-of-fit test is ____.

a) 9.49

b) 7.81

c) 7.78

d) 11.07

e) 12.77
Ans: a

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

Difficulty: Medium

39. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.

 Cars per 15 minute interval 0 1 2 3 4 >5 Observed Frequency 5 15 17 12 10 8

The observed value of chi-square for this goodness-of-fit test is _____.

a) 0.73

b) 6.72

c) 3.15

d) 7.81

e) 9.87
Ans: a

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

Difficulty: Hard

40. Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis.

 Cars per 15 minute interval 0 1 2 3 4 >5 Observed Frequency 5 15 17 12 10 8

Using a = 0.05, the appropriate decision for this goodness-of-fit test is ____.

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

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

c) do not reject the null hypothesis that the observed distribution is not Poisson

d) do not reject the null hypothesis that the observed distribution is Poisson

e) do nothing
Ans: d

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

Difficulty: Hard

41. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is: "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______.

a) p > 0.05

b) p = 0.05

c) m 30

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