Question 9.36

9.36 Plot the test statistic and the P-values.

Here is a two-way table of counts. The two categorical variables are and , 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 . 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.

0 1
0 50 50
1
  1. Consider setting equal to zero. Find the percent of zeros for the variable when . Do the same for the case where . With this choice of , the data match the null hypothesis as closely as possible. Explain why.
  2. Consider the tables where the values of are equal to 0, 5, 10, 15, 20, and 25. For each of these scenarios, find the percent of zeros for when . Notice that this percent does not vary with for .
  3. 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 given in part (b).
  4. Plot the values of the test statistic versus the percent of zeros for when . Do the same for the P-values. Summarize what you have learned from this exercise in a short paragraph.