Question

the dean of a major university claims that the mean number of hours students study at her university (per day) is less than 4.3 hours. if a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

a. there is not sufficient evidence to reject the claim ( mu = 4.3 )
b. there is sufficient evidence to support the claim ( mu = 4.3 ).
c. there is sufficient evidence to reject the claim ( mu = 4.3 )
d. there is not sufficient evidence to support the claim ( mu = 4.3 )

Explanation:

Step1: Understand hypothesis testing

In hypothesis testing, when we fail to reject the null hypothesis (\(H_0:\mu = 4.3\)), it means we do not have enough evidence from the sample data to say that the null hypothesis is false.

Step2: Analyze each option

• Option A: Failing to reject the null hypothesis \(H_0:\mu = 4.3\) implies there is not sufficient evidence to reject the claim \(\mu = 4.3\). This is correct.
• Option B: Failing to reject the null is not the same as supporting the null. Hypothesis testing is about not having enough evidence to reject, not about positively supporting in the sense of proving true.
• Option C: Since we failed to reject, we cannot say there is sufficient evidence to reject.
• Option D: The decision of failing to reject the null (\(H_0:\mu = 4.3\)) is not about supporting or not supporting \(\mu = 4.3\) in the sense of providing evidence for it. It is about lack of evidence to reject.

So the answer is A.

Answer:

A. There is not sufficient evidence to reject the claim \(\mu = 4.3\)