Question

Suppose a video teaching method will be adopted if a hypothesis test supports the conclusion that the video teaching method increases the mean grade point average (GPA) of students. Now, the mean GPA of students for the current face-to face teaching method is 3.04. Which of the following is FALSE?

Select one:

A. Type II error may be made when the hypothesis test concludes that the video teaching method will not be adopted but actually the mean GPA of students for the video teaching method is higher than 3.04.

B. At the 0.05 level of significance, the video teaching method will be adopted if the sample mean GPA for the video teaching method is found to be higher than 3.04

C. Type I error may be made when the hypothesis test concludes that the video teaching method will be adopted but actually the mean GPA of students for the video teaching method does not increase the GPA of students for the current face-to-face teaching method.

D. In this hypothesis test, H₀: μ ≤ 3.04 versus H₁: μ > 3.04

Answer 1

Solution:

The False statement is:

B. At the 0.05 level of significance, the video teaching method will be adopted if the sample mean GPA for the video teaching method is found to be higher than 3.04

Explanation:

Option A correctly describes the type II error.

Option C correctly describes the type I error.

Option D correctly mentions the null and alternative hypotheses for the given test.

But option B is not correct because just seeing the sample mean greater than 3.04 does not provide evidence against the null hypothesis. Therefore, to reject the null hypothesis, we need significant evidence against the null hypothesis at the 0.05 significance level.