Question

the mean age of bus drivers in chicago is greater than 53.4 years. 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 μ>53.4.
b. there is not sufficient evidence to support the claim μ>53.4.
c. there is sufficient evidence to support the claim μ>53.4.
d. there is sufficient evidence to reject the claim μ>53.4.

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of no - effect or no - difference. Here, if the claim is \(\mu>53.4\), the null hypothesis \(H_0:\mu\leq53.4\) and the alternative hypothesis \(H_a:\mu > 53.4\). When we fail to reject the null hypothesis, it means that the sample data does not provide enough evidence to support the alternative hypothesis. So, it implies that there is not sufficient evidence to support the claim \(\mu>53.4\).

Answer:

B. There is not sufficient evidence to support the claim \(\mu>53.4\).