An engineers union in Columbus, Ohio claims that the average pay for women working in the auto industry is $16/hr. A simple random sample of 9 women working in 1998 as engineers in the automotive industry in Columbus, Ohio revealed that the average pay rate was $15/ hr with a standard deviation of $2.
(a) Find a 99% confidence interval on the true mean pay rate of women engineers.
(b) What can you say about the union's claim? Write a sentence or two.