AnswersStatisticsTesting Claims about Means — TestQuestion 11
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Testing Claims about Means — Test

Question 11 • Statistics

The distribution of professional baseball player salaries has a mean of 3 point 2 dollars million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 50 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is 3 point 9 dollars million with a standard deviation of 2 point 1 dollars million. A significance test at an alpha level alpha is equal to 0 point 0 5 of produces a cap p -value of 0 point 0 2 What is the correct interpretation of the cap p -value?

Answer
A
Assuming the true mean salary is 3 point 2 dollars million, there is a 2 percent probability that the null hypothesis is true by chance alone.
B
Assuming the true mean salary is 3 point 2 dollars million, there is a 2 percent probability of getting a sample mean at least as extreme as 3 point 9 dollars million by chance alone.
C
Assuming the true mean salary is 3 point 2 dollars million, there is a 2 percent probability of getting a sample mean of 3 point 9 dollars million by chance alone.
D
Assuming the true mean salary is 3 point 2 dollars million, there is a 98 percent probability that a sample mean of 3 point 9 dollars million or one more extreme will occur by chance alone.

Explanation

A p-value is calculated assuming the null hypothesis is true—in this case, that the East Coast mean salary is $3.2 million. It is the probability of observing a sample result at least as extreme as the one obtained, in either direction because the analyst believes the mean is different. Thus, a p-value of 0.02 means a 2% probability of getting a sample mean at least as extreme as $3.9 million by chance alone. It does not mean the null hypothesis has a 2% probability of being true or that the sample mean must be exactly $3.9 million.

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