Question

The dean of a major university claims that the mean time for students to earn a Master's degree is at most 4.1 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? Question 22 options: There is sufficient evidence to reject the claim μ ≤ 4.1. There is not sufficient evidence to reject the claim μ ≤ 4.1. There is not sufficient evidence to support the claim μ ≤ 4.1. There is sufficient evidence to support the claim μ ≤ 4.1.

Answer 1

Failing to reject the null hypothesis means "There is not sufficient evidence to reject the claim μ ≤ 4.1," signaling insufficient evidence to support the alternative in the context of the dean's claim about the mean time to earn a Master's degree. Therefore correct option is B

Step-by-step explanation:

When a hypothesis test is performed, and the decision fails to reject the null hypothesis, it means that there is not sufficient evidence to contradict the established claim of the null hypothesis.

In this particular case, where the dean claims that the mean time for students to earn a Master's degree is at most 4.1 years (μ ≤ 4.1), if we fail to reject the null hypothesis, we interpret it as "There is not sufficient evidence to reject the claim μ ≤ 4.1."

This interpretation falls in line with standard statistical testing procedures where failing to reject the null indicates a lack of evidence to support the alternative hypothesis, rather than unequivocal proof of the null hypothesis's claim.