Question

A university will add fruit juice vending machines to its classroom buildings if the student body president is convinced that more than 20 percent of the students will use them. A random sample of n students will be selected and asked whether or not they would use the vending machines. A large-sample test for proportions at the significance level of α = 0.05 will be performed. The null hypothesis that the proportion of all students who would use the vending machines is 20 percent will be tested against the alternative that more than 20 percent of all students would use them. For which of the following situations would the power of the test be highest?

Answer 1

e). the sample size is n = 1000 and 50 percent of all students use the vending machines.

Explanation:

The efficiency of the test would be highest when the sample size includes a minimum of 1000 samples and at least half of the students must use them. Conducting the test under such conditions would make it impactful and show if the idea would be successful and beneficial or not. If a lesser percentage of students use it, its investment might be difficult to recover or if the test is conducted with a smaller population, the results or outcomes might not be reliable or trustworthy for representing the entire population. Thus, option e shows the correct situations.