Question

The manager of a health maintenance organization has set a target the mean waiting time of nonemergency patients to not exceed 30 minutes. In spot checks, manager finds the waiting times for 22 patients; the patients are selected randomly on different days. Assume that the population standard deviation of waiting times is 10 minutes. Suppose that sample mean waiting time is 38.1 minutes and test the claim at 4% SL. Complete hypothesis testing has to be shown, including the interpretation of obtained result.[

Answer 1

As we are given the population standard deviation here as 10 minutes, therefore this is a case of a standard normal test. As we are testing whether the mean is greater than 30, the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

As this is a one sided test, the p-value here is obtained from the standard normal tables as:
p = P(Z > 3.8) = 0.0001

As the p-value here is 0.0001 < 0.04 which is the level of significance, we can reject the null hypothesis here and conclude that the test is significant and therefore we have sufficient evidence here to conclude that the mean is greater than 30.