Suppose that we wish to test the null hypothesis that for 3 cells, A, B, and C, the cell categories are equal. We observed 8 data in cell A, 13 in cell B, and 9 in cell C. What is the decision rule using the 0.05 significance level?
A) 7.815
B) 5.991
C) 43.773
D) 42.557

Question

Suppose that we wish to test the null hypothesis that for 3 cells, A, B, and C, the cell categories are equal. We observed 8 data in cell A, 13 in cell B, and 9 in cell C. What is the decision rule using the 0.05 significance level? 
A) 7.815
B) 5.991
C) 43.773
D) 42.557

Quizplus · Accepted Answer

To test the null hypothesis, we can use the chi-square test of independence. With 3 cells, we have 2 degrees of freedom. Using a significance level of 0.05, the critical value of chi-square with 2 degrees of freedom is 5.991. If the calculated chi-square value is greater than 5.991, we reject the null hypothesis in favor of the alternative hypothesis that at least one cell category is different from the others. The calculated chi-square value can be found using a chi-square calculator or software.

Suppose That We Wish to Test the Null Hypothesis That