Question

identify the correct alternative hypothesis.
a state university annual report showed that its retention rate was at 24% and university administrators would like to increase this rate. after implementing several new programs during the last two years, the university reevaluated its retention rate.
what is the correct alternative hypotheses for a test to determine whether the retention rate has increased during the last two years?
○ ha: p>0.24
○ ha: p≠0.24
○ ha: p<0.24

Explanation:

Step1: Understand the hypothesis test

In hypothesis testing for proportion, the null hypothesis \(H_0\) is usually a statement of no change. Here, the original retention rate is \(p = 0.24\). The alternative hypothesis \(H_a\) is what we want to test. Since the university wants to know if the retention rate has increased, we are looking for a one - sided (right - tailed) test.

Step2: Formulate the alternative hypothesis

For a right - tailed test about a proportion \(p\), the alternative hypothesis is \(H_a:p>0.24\)

Answer:

\(H_a:p > 0.24\)