19. A researcher is conducting a Chi 2 test for Independence to evaluate the rel

Question

19. A researcher is conducting a Chi2 test for Independence to evaluate the relationship between gender and preference for four different designs for a new automobile. Each individual in a sample of n = 40 males and n = 40 females selects a favorite design from the four choices. If the researcher obtains a Chi2 = 9.81, what is the appropriate statistical decision for the test?

A. Reject the null hypothesis with = .05 but not with = .01 B. Reject the null hypothesis with either = .05 or = .01 C. Fail to reject the null hypothesis with either = .05 or = .01 D. There is not enough information to determine the appropriate decision.

Explanation / Answer

For gender, there are a = 2 categories.

For auto, there are b = 4 categories.

Hence,

df = (a-1)(b-1) = 3

As chi^2 = 9.81, then by using tables,

chi^2(0.05) = 7.815 (reject Ho)
chi^2(0.01) = 11.345 (do not reject Ho)

Hence,

OPTION A. Reject the null hypothesis with = .05 but not with = .01 [ANSWER]

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