A simple random sample of 40 salaries of NCAA football coach

A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953. Assume that =$463,364. a.) Find the best point estimate of the mean salary of all NCAA football coaches. b.) Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach. c.) Does the confidence interval contain the actual population mean of $474,477?

Solution

n =40

Sample Mean = $415,953.

SD =$463,364

a)

Best point estimate of the mean salary = $415,953. Answer

b)

z for 95% confidence interval =1.96

Margin of error = z * SD /sqrt(n)

= 1.96*463,364 / sqrt(40)

= 143597.99

Confidence Interval :

(415953 - 143597.99 , 415953 + 143597.99  )

=( 272355.01 , 559550.99) Answer

c)

Yes , the confidence interval contain the actual population mean of $474,477.