Question: The hourly wages in the aircraft industry vary normally with a standard deviation of $3.20.

A random sample of 10 aircraft industry workers is selected, with their hourly wages as follows: $15.20, $9.94, $12.28, $14.99, $23.80, $16.42, $12.71, $18.22, $21.10, $13.20.

(a) Find a 90% confidence interval for the mean hourly wage for all workers in the aircraft industry.

(b) If we find a confidence interval, what kind of interval should we calculate here? Why? Report your interval by completing the sentence "We are 90% confident that . . . ."

(c) If we need to reduce the margin of error (E) for this confidence interval to $1, how large a sample must we have? [Remember, z for a 90% CI is 1.645 and n=[(z*sigma)/E)^2].