Independent random samples of n, = 180 and n2 = 180 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 95 successes, and sample 2 had 101 successes. (a) Suppose you have no preconceived idea as to which parameter, p, or p,, is the larger, but you want to detect only a difference between the two parameters if one exists. What should you choose as the alternative hypothesis for a statistical test? The null hypothesis? O Ho: (P1 - P2) = 0 versus Ha: (P1 - P2) 0 O Ho: (P1 - P2) = 0 versus Ha: (P1 - P2) > 0 (b) Calculate the standard error of the difference in the two sample proportions, (P1 - P2). Make sure to use the pooled estimate for the common value of p. (Round your answer to four decimal places.) (c) Calculate the test statistic that you would use for the test in part (a). (Round your answer to two decimal places.) Based on your knowledge of the standard normal distribution, is this a likely or unlikely observation, assuming that Ho is true and the two population proportions are the same? O This is an unlikely observation if He is true, since it lies less than one standard deviation below (P, - P2) = 0. O This is a likely observation if Ho is true, since it lies more than one standard deviation below (P, - P2) = 0. O This is a likely observation if Ho is true, since it lies less than one standard deviation below (P] - P2) = 0. O This is an unlikely observation if Ho is false, since it lies more than one standard deviation below (P1 - P2) = 0. O This is a likely observation if Ho is false, since it lies more than one standard deviation below (P1 - P2) = 0. (d) p-value approach: Find the p-value for the test. (Round your answer to four decimal places.) p-value = Test for a significant difference in the population proportions at the 1% significance level. O Ho is rejected. There is insufficient evidence to indicate that there is a difference in the two population proportions. O Ho is rejected. There is sufficient evidence to indicate that there is a difference in the two population proportions. O Ho is not rejected. There is sufficient evidence to indicate that there is a difference in the two population proportions. O Ho is not rejected. There is insufficient evidence to indicate that there is a difference in the two population proportions. (e) Critical value approach: Find the rejection region when a = 0.01. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused region.) 2> Do the data provide sufficient evidence to indicate a difference in the population proportions? O Ho is rejected. There is insufficient evidence to indicate that there is a difference in the two population proportions. O Ho is not rejected. There is sufficient evidence to indicate that there is a difference in the two population proportions. O Ho is not rejected. There is insufficient evidence to indicate that there is a difference in the two population proportions. O Ho is rejected. There is sufficient evidence to indicate that there is a difference in the two population proportions