Question

Interpreting a P-value A student performs a test of $\mathrm{H}0:\mathrm{p}=0.3H_0:p=0.3$versus Ha:$\mathrm{p}<0.3H_a:p<0.3$and gets a $P$-value of $0.22$The student says, "This means there is about a$22\%$chance that the null hypothesis is true." Explain why the student's explanation is wrong.

Short answer

There is a$22\%$ possibility of getting the sample result or less by chance alone, when the null hypothesis$H_0:p=0.3$is true.

Step-by-step solution

Step 1:Given information

Interpreting a P-value A student performs a test of $\mathrm{H}0:\mathrm{p}=0.3H_0:p=0.3$versus Ha:$\mathrm{p}<0.3H_a:p<0.3$and gets a P-value of$0.22$. The student says, "This means there is about a$22\%$ chance that the null hypothesis is true." Explain why the student's explanation is wrong.

Step 2:Explaination

$P=0.22=22\%$

$H_0:p=0.3$

$H_a:p<0.3$

The $p$-value is the probability of getting the value of the test statistic, or a value more extreme, when the null hypothesis is true.

It is observed that there are two issues with the given interpretation is that the probability is not about the null hypothesis being true. But the probability should be about the sample results.

There is a $22\%$ possibility of getting the sample result or less by chance alone, when the null hypothesis$H_0:p=0.3$ is true.