Plot the test statistic and the P-values. Here is a 2 3 2 two-way table of counts. The two categorical variables are U and V, and the possible values for each of these variables are 0 and 1. Notice that the second row depends upon a quantity that we call

a. For this exercise, you will examine how the test statistic and its corresponding P-value depend upon this quantity. Notice that the row sums are both 100.

V U 0 1 0 50 50 1 50 1 a 50 2 a

(a) Consider setting a equal to zero. Find the percent of zeros for the variable V when U 5 0. Do the same for the case where U 5 1. With this choice of

a, the data match the null hypothesis as closely as possible. Explain why.

(b) Consider the tables where the values of a are equal to 0, 5, 10, 15, 20, and 25. For each of these scenarios, find the percent of zeros for V when U 5 1. Notice that this percent does not vary with a for U 5 0.

(c) Compute the test statistic and P-value for testing the null hypothesis that there is no association between the row and column variables for each of the values of a given in part (b).

(d) Plot the values of the X2 test statistic versus the percent of zeros for V when U 5 1. Do the same for the P-values. Summarize what you have learned from this exercise in a short paragraph.