(a) Given a population standard deviation of $6,000 and a sample mean salary of $80,100 for a random sample of 100 female members, construct a 99 percent confidence interval for the mean salary for all female members.

(b) Given this confidence interval, is there any consistent evidence that the mean salary for all female members falls below $82,500, the mean salary for all members?

Now the answers the back of the book gave me were:

(a) 80,100 +- 2.58 [6,000 / radical 100] = {8,648; 78,552}

(b) We can claim with 99 percent confidence, that the interval between $78,552 and $81,648 includes the true population mean salary for all female members of the American Psychlogical Association. All of these values suggest that, on average, females' salaries are less than males' salaries.