Question

1. What is the degree of freedom, df of Chi² for Independence, if each nominal variable consists of 4 categories?

• A. df = 2

• B. df = 8

• C. df = 7

• D. df = 4

• E. df = 9

• F. df = 6

2. A researcher used Chi² test for Goodness of Fit to test whether there is any difference in preferences for brands of six soft drinks. If the study uses a sample of n = 180 participants, what is the expected frequency for each brand of soft drink?

• A. 25

• B. 36

• C. 20

• D. 15

• E. 30

• F. 90

3. A researcher used Chi² for Independence to evaluate if there is a significant relationship between gender (i.e., male vs. female) and choice among fifteen academic majors. If the computed Chi² = 22.56, what is the correct statistical decision for the outcome of this test?

• A. Fail to reject the null hypothesis with either p < .05 or p < .01

• B. Reject the null hypothesis with p < .05 but not with p <.01

• C. Fail to reject the null hypothesis with p < .05 but not with p <.01.

• D. Reject the null hypothesis with either p < .05 or p <.01

4. Under what conditions is phi-coefficient used to measure effect size for a Chi² for Independence?

• A. When both variables consist of more than two categories.

• B. None of the above.

• C. When one of two variables consist of more than two categories.

• D. When both variables consist of exactly two categories.

Answer 1

1) Answer: E) df = 9 Explanation: df=(c-1)(-1)=(4-1)(4-1)=9 2) Answer: E) 30 Explanation: Expected frequency 180 N =-= 6 30 6 3) Answer: A) Fail to reject the null hypothesis with either p<.05 or p<.01 Explanation: The df = (c-1)(r-1)=(2-1)(15-1)=14 The p-value of chi-square at 14 df = 0.0678 Conclusion: The p-value of chi-square test is greater than 0.05 and 0.01. Hence we fail to reject the null hypothesis with either p<.05 or p<.01 4) Answer: D) When both variables consist of exactly two categories.