Question

the dean of a major university claims that the mean time for students to earn a masters degree is at most 3.9 years. if a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
a. there is sufficient evidence to support the claim μ ≤ 3.9.
b. there is not sufficient evidence to reject the claim μ ≤ 3.9.
c. there is not sufficient evidence to support the claim μ ≤ 3.9.
d. there is sufficient evidence to reject the claim μ ≤ 3.9.

Explanation:

In hypothesis testing, failing to reject the null hypothesis means that the data does not provide enough evidence to go against the null hypothesis. Here, the claim is \(\mu\leq3.9\) (which would be the null hypothesis in this context). So, not rejecting it implies there isn't enough evidence to reject the claim \(\mu\leq3.9\).

Answer:

B. There is not sufficient evidence to reject the claim \(\mu\leq3.9\).