Question

A large university wants to determine if they should build another cafeteria. They plan to survey a sample of their students to verify the claim that the overall proportion interested in a meal plan is higher than 40%, in which case they will consider building a new cafeteria. Let p represent the proportion of students interested in a meal plan. Here are the hypotheses they'll use: H0: p ≤ 0.40; Ha: p > 0.40 What would be the consequence of a Type II Error in this context? Select one: They don't consider building a new cafeteria when they shouldn't. They consider building a new cafeteria when they should. They consider building a new cafeteria when they shouldn't. They don't consider building a new cafeteria when they should.

Answer 1

The consequence of a type II error will be that they don't consider building a new cafeteria when they should.

Explanation:

This hypothesis test aims to investigate whether the overall proportion of students interested in a meal plan is higher than 40%. If the proportion of students that are interested in a meal plan is indeed higher than 40%, the university will consider building a new cafeteria.

The null hypothesis is given as

H₀: p ≤ 0.40

And interpreted as the overall proportion of students interested in a meal plan being less than or equal to 40%. If this hypothesis holds, the university will not consider building a new cafeteria.

The alternative hypothesis is given as

Ha: p > 0.40

And it is interpreted as the overall proportion of students interested in a meal plan being higher than 40%. If this hypothesis holds, the university will consider building a new cafeteria.

In Hypothesis testing, a type II error involves failing to reject the null hypothesis when in reality it should have been rejected.

It entails not rejecting the null hypothesis and making conclusions based on the null hypothesis, when in reality, the alternative hypothesis should have been accepted together with its conclusion.

So, not rejecting the null hypothesis for this qiestion would mean that the hypothesis test gave a result that indicated the overall proportion of students interested in a meal plan is less than or equal to 40% and the conclusion drawn would have been that the University will not consider building a new cafeteria when in reality, the alternative hypothesis holds, the null hypothesis should have been rejected, the overall proportion of students interested in a meal plan is greater than 40% and the right consequence or conclusion would be for the University to consider building a new cafeteria.

It is evident that option D is correct.

The consequence of a type II error will be that the University don't consider building a new cafeteria when they should.

Hope this Helps!!!