The business college computing center wants to determine the proportion of business students who have personal computers (pcʹs) at home. if the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. suppose 200 business students were randomly sampled and 65 have pcʹs at home. find the rejection region for this test using α = 0.01.

By considering the given information, we have

, since the alternative hypothesis is right tail, so the test is a right tail test.

Given : Sample size : n= 200

Number of students have PC's in their home  = 65

Then,

Test statistic :

Using the standard normal distribution table for z, we have

P-value for right tail test  :

Since the p-value is less that the significance level (), so we reject the null hypothesis.

Hence, we have evidence to reject the null hypothesis i.e. we may support the alternative hypothesis that the proportion exceeds 25%.