A copy shop records that in n = 64 cases, the cartridge for the copy machine lasted an average of 18300 copies with a standard deviation of 2800 copies. Assume that the population is normal. 

(a)  Obtain a 95% confidence interval for u, the population mean number of copies before a new cartridge is needed for the copy machine. Does u lie in your interval obtained from the data? Explain.

(b) Conduct a test of hypotheses with the intent of showing that the mean number of copies is greater than 17500 copies at a = 0.02 significant level. What error could you have made? Explain