Question

the mean iq of statistics teachers is greater than 160. 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 support the claim \\( \mu>160 \\).
b. there is sufficient evidence to reject the claim \\( \mu>160 \\).
c. there is not sufficient evidence to reject the claim \\( \mu>160 \\).
d. there is sufficient evidence to support the claim \\( \mu>160 \\).

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is the statement being tested. Here, if the claim is \(\mu> 160\), the null hypothesis \(H_0:\mu\leq160\) and the alternative hypothesis \(H_1:\mu > 160\). Failing to reject the null hypothesis means that the sample data does not provide enough evidence to support the alternative hypothesis.

Answer:

A. There is not sufficient evidence to support the claim \(\mu>160\)