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Chapter 9: Q .13. (page 564)

Interpreting a P-value A student performs a test of H0:渭=100H0:渭=100versus Ha: 渭>100Ha:渭>100and gets a P-value of 0.044.The student says, "There is a0.044 probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.

Short Answer

Expert verified

- 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

01

Step 1:Given information

Interpreting a P-value A student performs a test of $H0:渭=100H0:渭=100versusHa:渭>100Ha:渭>100and gets a P-value of0.044. The student says, "There is a0.044probability of getting the sample result I did by chance alone."

02

Step 2:Explaianation

P=0.044=4.4%

H0:渭=100

Ha:渭>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.

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