A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile.Each individual in a sample of n = 30 males and n = 30 females selects a favorite design from the three choices.If the researcher obtains a chi-square statistic of χ² = 4.81,what is the appropriate statistical decision for the test?
A)Reject the null hypothesis with α = .05 but not with α = .01
B)Reject the null hypothesis with either α = .05 or α = .01
C)Fail to reject the null hypothesis with either α = .05 or α = .01
D)There is not enough information to determine the appropriate decision.

Question

Quizplus · Accepted Answer

The degrees of freedom for the test are (3-1)(2-1) = 2. The critical value for χ² with 2 degrees of freedom at α = .05 is 5.991 and at α = .01 is 9.210. Since 4.81 is less than both critical values, we fail to reject the null hypothesis at both significance levels.

A Researcher Is Conducting a Chi-Square Test for Independence to Evaluate