Question

the mean monthly gasoline bill for one household is greater than $150. 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=$ 150)
b. there is not sufficient evidence to support the claim (mu=$ 150)
c. there is sufficient evidence to support the claim (mu=$ 150)
d. there is sufficient evidence to reject the claim (mu=$ 150)

Explanation:

Step1: Set up hypotheses

The null hypothesis \( H_0:\mu = 150 \), the alternative hypothesis \( H_a:\mu>150 \)

Step2: Analyze decision

When we fail to reject the null hypothesis \( H_0 \), it means that based on the sample data and the hypothesis - testing procedure, we do not have enough evidence to say that the null hypothesis is false. In this case, we do not have enough evidence to reject \( \mu = 150 \) (the claim in the null hypothesis). Options B and C are about supporting \( \mu>150 \) (the alternative hypothesis), which is not relevant when we fail to reject the null. Option D is incorrect because failing to reject the null is not about having sufficient evidence to reject the null.

Answer:

A. There is not sufficient evidence to reject the claim \( \mu=\$150 \)