Solve the following.

Question

Compute the value of the test statistic for each test using the given information.

1. Testing Ho: p = 0.48 vs Ha: p <0.48 at a = 0.10, n = 540, p = 0.58

2. Testing Ho: p = 0.94 vs Ha: p > 0.94 at a = 0.025, n = 1200, p = 0.96.

3. Testing Ho: p = 0.36 vs Ha:P 0.36 at a = 0.05, n = 1300, p = 0.40.

B. For each test above, construct the rejection region given the respective significance level and make the decision based on your answer.

Answer 1

z = (p - phat)/sqrt(p * (1-p)/n), where p is population proportion under Ho, phat is sample proportion and n is sample is size

1. z = (0.58 - 0.48)/sqrt(0.48 * 0.52/540) = 4.65

rejection region is z corresponding to below probability 0.1 = z < -2.33

do not reject Ho

2. z = (0.96 - 0.94)/sqrt(0.94 * 0.06/1200) = 2.92

rejection region is z corresponding to above probability 1 - 0.025 = 0.975 = z > 1.96

reject Ho

3 z = (0.40 - 0.36)/sqrt(0.36 * 0.64/1300) = 3

if Ha is p != 0.36, then rejection region is z corresponding to above probability 0.975 and below probability 0.025 = z > 1.96 or z < -1.96 = |z| > 1.96

reject Ho