Question: ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. But if too much cash is unnecessarily kept in the ATMs, the bank is forgoing the opportunity of investing the money and earning interest. Suppose that at a particular branch, the population mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160, with a population standard deviation of $30.
a. If a random sample of 36 customer transactions indicates that the sample mean withdrawal amount is $172, is there evidence to believe that the population mean withdrawal amount is no longer $160? (Use a 0.05 level of significance.)
b. Compute the p-value and interpret its meaning.
c. What is your answer in (b) if you use a 0.01 level of significance?
d. What is your answer in (b) if the standard deviation is $24 (use α = 0.05)?