Test the following claim. Identify the null hypothesis, alternative hypothesis,

Question

Test the following claim. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim.

A simple random sample of 40 salaries of professional football coaches has a mean of $414,443. The standard deviation of all salaries of professional football coaches is $469,925. Use a 0.01 significance level to test the claim that the mean salary of a professional football coach is less than $500,000.

Explanation / Answer

null hypothesis: mean = 500000 alternative hypothesis: mean < 500000 test statistic: z = (414443-500000)/(469925/sqrt(40)) = -1.15 critical value: z = -2.546 |-1.15| < |-2.546| so we fail to reject the null hypothesis no evidence that mean is less than 500,000

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