Question

suppose you want to test the claim that $\mu_1 = \mu_2$. two samples are randomly selecte hypothesis test is performed, how should you interpret a decision that rejects the nu
a. there is sufficient evidence to reject the claim $\mu_1 = \mu_2$.
b. there is sufficient evidence to support the claim $\mu_1 = \mu_2$.
c. there is not sufficient evidence to support the claim $\mu_1 = \mu_2$.
d. there is not sufficient evidence to reject the claim $\mu_1 = \mu_2$.

Explanation:

In hypothesis testing, the null hypothesis (here, the claim \(\mu_1 = \mu_2\)) is tested. If we reject the null hypothesis, it means there is sufficient evidence against the null hypothesis (the claim \(\mu_1=\mu_2\)). So the correct interpretation is that there is sufficient evidence to reject the claim \(\mu_1 = \mu_2\).

Answer:

A. There is sufficient evidence to reject the claim \(\mu_1 = \mu_2\).