Question

A well known bank stores enough money during the weekends to satisfy its customers needs. The expected average withdrawal during the weekend is $550 with a standard deviation of $70. When they looked at a sample of the last 36 weekend transactions, they found the average withdrawal to be $600. At α=0.05, is there evidence that the mean withdrawal has increased during weekends? (Z0.05=1.645, Z0.025=1.96)

Answer 1

The mean withdraw has increased during weekend.

Step-by-step explanation:

Assume that the withdraw amounts are normal distributed. To test whether the mean withdrawal has increased during weekends, we take a z-test. The z-test is possible because the observed sample (weekend transactions) is greater than 30.

The null hypothesis (
`H_(0)`) is when the mean withdrawal is greater than 550. The alternative hypothesis (
`H_(A)`) is when the mean withdrawal is equal to 550 or smaller. At an alpha of 0.05% is selected with a two-tailed test, , there is 0.025% of the samples in each tail, and the alpha has a critical value of 1.96 or -1.96. If the z-value is greater than 1.96 or less than -1.96, the null hypothesis is rejected.

z-value = (600-550) / 70 / 36^(1/2) = 0.1190

At α=0.05, the z-value < 1.96 and > -1.96, the null hypothesis is not rejected. Therefore, the mean withdraw has increased during weekend.