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)

The mean withdraw has increased during weekend.

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 () is when the mean withdrawal is greater than 550. The alternative hypothesis () 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.

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