Question

Making conclusions A student performs a test of $H_0:p=0.75$versus $H_a:p<0.75$at $\alpha =0.05$significance level and gets a $P$-value of $0.22$

The student writes: “Because the P-value is large, we accept $H_0$. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Short answer

As $P$value is large, we cannot reject$H_0$. Null hypothesis is not false.

Step-by-step solution

Given Information

It is given that $P=0.22=22\%$

$\alpha =0.05$

$H_0:p=0.75$

$H_1:p<0.75$

Explanation

If $P\mathrm{value}<\alpha$, reject null hypothesis

Here it is not fulfilled as $0.22>0.05\Rightarrow \text{Fail to reject}{H}_0$

The statement having issues are:

• Never accepting $H_0$
• There is never convincing proof that null hypothesis is true, instead it can be that null hypothesis is not true.