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 regarding the null hypothesis?
A) Do not reject the null hypothesis.
B) Reject the null hypothesis.
C) There is not enough information to reach a decision.

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 regarding the null hypothesis? 
A) Do not reject the null hypothesis.
B) Reject the null hypothesis.
C) There is not enough information to reach a decision.

Quizplus · Accepted Answer

The chi-square test for independence is used to test the null hypothesis that the cell categories are equal. The chi-square statistic is calculated as:```χ² = Σ (O - E)² / E```where O is the observed frequency and E is the expected frequency.The expected frequency for each cell is calculated as:```E = (row total * column total) / grand total```The grand total is the sum of all the observed frequencies.In this case, the row totals are 8, 13, and 9, the column totals are 8, 13, and 9, and the grand total is 30.The expected frequencies are:```E(A) = (8 * 8) / 30 = 2.13E(B) = (8 * 13) / 30 = 3.47E(C) = (8 * 9) / 30 = 2.40```The chi-square statistic is:```χ² = [(8 - 2.13)² / 2.13] + [(13 - 3.47)² / 3.47] + [(9 - 2.40)² / 2.40] = 10.64```The degrees of freedom for the chi-square test is (r - 1) * (c - 1), where r is the number of rows and c is the number of columns. In this case, r = 3 and c = 3, so the degrees of freedom is 4.The critical value for the chi-square test with 4 degrees of freedom and a significance level of 0.05 is 9.488.Since the chi-square statistic (10.64) is greater than the critical value (9.488), we reject the null hypothesis and conclude that the cell categories are not equal.

Suppose That We Wish to Test the Null Hypothesis That