Question

A random sample of 30 MBAs working in Chicago revealed that their mean annual salary was $75,000. Suppose that the population standard deviation σ is $8,000 but that the population mean µ is unknown.

a. What is the point estimate of the mean salary µ of all MBAs in this city? As always, don't use neither the dollar sign $ nor comas (Duh!)

b. What is the probability that point estimates such as this one will be within $2,500 of the mean salary µ of all MBAs? Answer

Answer 1

a. The point estimate for the mean salary µ of all MBAs in this city is 75000.

b. Here the population standard deviation σ is known to be $8,000. Thus the confidence interval for µ of level (1-)100% is given by:

. Now here we want the point estimate to be within $2,500 of the mean salary µ of all MBAs, i.e. error term within $2500. Hence we have:

, Thus the probability is 1- = 0.913