Question

Making conclusions A student performs a test of $H_0:\mu =12$versus $H_a:\mu \ne 12$

at the $\alpha =0.05$significance level and gets a $P$-value of $0.01$. The

student writes: “Because the $P$-value is small, we reject $H_0$. The data prove that $H_a$is true.” Explain what is wrong with this conclusion.

Short answer

The data do not show that $H_1$is true, it show that alternative hypothesis $H_1$is true.

Step-by-step solution

Given Information

It is given that $p=0.01$

$\alpha =0.05$

$H_0:\mu =12$

$H_1:\mu \ne 12$

Explanation

As $0.01<0.05\Rightarrow \text{Reject}{H}_0$

There is convincing evidence that null hypothesis is not true.

Issue with statement is:

• Data do not convince that $H_1$is true.
• It shows that alternative hypothesis$H_1$is true.