ATMs must be stocked with enough cash to satisfy customers m

ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. However, if too much cash is unnecessarily kept in the ATMs, the bank is foregoing 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 Suppose that at a particular branch the population mean amount of money withdrawn from ATMs per customer transaction over the weekend has historically been $140 with a population standard deviation of $30. The branch manager selects a random sample of 50 ATM transactions to test whether the population mean withdrawal amount has changed. The mean of the sample was $136.00. Using the 0.10 level of significance, test the claim being made using the critical value approach to hypothesis testing. Also, compute the p-value and interpret its meaning. Explain your conclusion.

Solution

As n=50>30, we can assume the distribution to be a standard normal distribution.

Therefore, we shall compute the z statistic

Z=(136-140)/(30/sqrt(50)) = -0.942

Critical Z value = Z(0.05) (Assuming a two tailed test)

Z(0.05) = -1.64

As the computed Z is greater than the critical Z, we conclude that the test is not significant, that is, we fail to reject the null hypothesis.

p value = 0.17

Interpretation: As the p value is greater than the level of significance, it means that we cannot reject the null hypothesis, or, the given sample mean does not lie beyond the significant region.