Testing \(H_{0}: p_{1}=p_{2}\) vs \(H_{a}: p_{1}>p_{2}\) using \(\hat{p}_{1}-\hat{p}_{2}=0.45-0.30=0.15\) with each of the following sample sizes:

(a) \(\hat{p}_{1}=9 / 20=0.45\) and \(\hat{p}_{2}=6 / 20=0.30\)

(b) \(\hat{p}_{1}=90 / 200=0.45\) and \(\hat{p}_{2}=60 / 200=0.30\)

(c) \(\hat{p}_{1}=900 / 2000=0.45\) and \(\hat{p}_{2}=600 / 2000=0.30\)

The same sample statistic is used to test a hypothesis, using different sample sizes. In each case, use StatKey or other technology to find the p-value and indicate whether the results are significant at a 5\% level. Which sample size provides the strongest evidence for the alternative hypothesis?