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Chapter 9: Q .14. (page 564)

Interpreting a P-value A student performs a test of H0:p=0.3H0:p=0.3versus Ha:p<0.3Ha:p<0.3and gets a P-value of 0.22The student says, "This means there is about a22%chance that the null hypothesis is true." Explain why the student's explanation is wrong.

Short Answer

Expert verified

There is a22% possibility of getting the sample result or less by chance alone, when the null hypothesisH0:p=0.3is true.

Step by step solution

01

Step 1:Given information

Interpreting a P-value A student performs a test of H0:p=0.3H0:p=0.3versus Ha:p<0.3Ha:p<0.3and gets a P-value of0.22. The student says, "This means there is about a22% chance that the null hypothesis is true." Explain why the student's explanation is wrong.

02

Step 2:Explaination

P=0.22=22%

H0:p=0.3

Ha: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 hypothesisH0:p=0.3 is true.

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