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Z test for mean amount of money withdrawn from ATMs.

ATMs should be stocked with sufficient cash to satisfy customers making withdrawals over an entire weekend. But if too much cash is kept unnecessarily in ATMs, bank is forgoing the opportunity of investing the money and earning interest. Assume that at a particular branch, population mean amount of money withdrawn from ATMs per customer per transaction over the weekend is $160, with a population standard deviation of $30.

If a random sample of 36 customer transactions indicates that 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.)

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