CH ALLENGE Sample size and the P-value. In this exercise we examine the effect of the sample size on the significance test for comparing two proportions. In each case suppose that ˆp1 = 0.5 and

ˆp2 = 0.4, and take n to be the common value of n1 and n2. Use the z statistic to test H0: p1 = p2 versus the alternative Ha: p1 = p2. Compute the statistic and the associated P-value for the following values of n: 40, 50, 80, 100, 400, 500, and 1000. Summarize the results in a table. Explain what you observe about the effect of the sample size on statistical significance when the sample proportions ˆp1 and ˆp2 are unchanged.