Question

Interpreting a $\mathit{P}$-value A student performs a test of $\mathrm{H}0:\mu =100H_0:\mu =100$versus Ha: $\mu >100H_a:\mu >100$and gets a $P$-value of $0.044.$The student says, "There is a$0.044$ probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.

Short answer

- The interpretation is not given that the probability only carries when the null hypothesis is true.

- The interpretation is not given that the sample results can be more extreme (larger) as well.

Step-by-step solution

Step 1:Given information

Interpreting a P-value A student performs a test of $$\mathrm{H}0:\mu =100H_0:\mu =100$$versusHa:$$\mu >100H_a:\mu >100$and gets a P-value of$0.044$. The student says, "There is a$0.044$probability of getting the sample result I did by chance alone."

Step 2:Explaianation

$P=0.044=4.4\%$

$H_0:\mu =100$

$H_a:\mu >100$

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 of the P-value:

- The interpretation is not given that the probability only carries when the null hypothesis is true.

- The interpretation is not given that the sample results can be more extreme (larger) as well.