Question

The policy of a particular bank branch is that its ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. The expected average amount of money withdrawn from ATM machines per customer transaction over the weekend is $160 with an expected standard deviation of $34. (Assume that this distribution is normal). Suppose that a random sample of 26 customer transactions is examined and it is observed that the mean withdrawal is $171. Draw a fully justified conclusion based on this setup. Be sure to interpret your p-value.

Answer 1

Solution:

If a random sample of 26 customer transactions indicates that the sample mean withdrawal amount is $171, is there evidence to believe that the population mean withdrawal amount is no longer $160? (Use a 0.05 level of significance.)

Hypotheses: $H_{0}$: µ = $160

                      $H_{1}$: µ ≠ $160

Critical Value:

Since population standard deviation is known, use Z statistic.

For a two-tailed test and at the 0.05 level of significance, $Z_{cv}$= +1.96.

Test Statistics: Decision and Conclusions:

Decision rule: Reject $H_{0}$ if -$Z_{Stat}$< –1.96 or $Z_{Stat}$> +1.96.

Since $Z_{Stat}$= 2.4 > 1.96, reject $H_{0}$.

There is enough evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.