A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference among 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)Fail to reject the null hypothesis with α = .10.

Question

Quizplus · Accepted Answer

The researcher obtained a chi-square statistic of 4.81. The degrees of freedom for this test are (number of rows - 1) * (number of columns - 1) = (2)(3) = 6. Using a chi-square distribution table with 6 degrees of freedom, the critical values for α = .05 and α = .01 are 12.59 and 16.81, respectively. Since the obtained statistic is less than these critical values, we fail to reject the null hypothesis. Therefore, the appropriate statistical decision is to fail to reject the null hypothesis with either α = .05 or α = .01.

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

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