Question

5) A contingency table of the number of individuals taking a certain final exam stratifying by the students' grades (prior to taking the final) is included below. A B с F 1 Taking exam Not taking exam 2 36 38 22 18 14 1 15 0 39 55 94 40 1 a) Explain to me in one sentence why the results from a xtest for independence might not be reliable. Hint, some software would tell you explicitly what the problem is (if you ran the analysis) other software will simply tell you that ": Chi-squared approximation may be incorrect" b) A y test for independence between pre-grade and choice of whether to take the exam was conducted. The observed test statistic was Xổos = 41.569. State the null hypothesis of this test, determine what conclusion to draw with respect to the null and interpret your conclusion within the context of the problem.

Answer 1

a.) The test might not be reliable because for the chi-square test of independence, we must have each cell frequency to be 5 or greater than 5. But, here we observe that the cell frequency is smaller than 5 in 3 cells.

b.) Null hypothesis: There is no significant association between student grades and whether or not he takes the certain final exam.

Test statistic = 41.569

p-value = Probability (chi square > 41.569) < 0.05

so we reject the null hypothesis at alpha = 0.05 level of significance and conclude that there is significant association between student's grades and whether or not they take the final exam.