Each patient of Aloha Memorial Hospital is asked to evaluate the service at the time of release. Recently there have been complaints that resident physicians and nurses on the surgical wing respond too slowly to calls of senior citizens. In fact, it is claimed that the other patients receive faster service. Mr. Armstrong, president of the hospital, asked the quality assurance department to investigate. After studying the situation, the quality assurance department collected the following data.

at a 99% confidence level?

Solution: We need to test

We need a right-tailed t-test. We get the following table with the calculations:

The t-statistics is t = 3.432, and the corresponding p-value is p = 0.000388. Since the p-value is less than the significance level, we reject the null hypothesis. That implies that we have enough evidence to support the claim that the mean response time is longer for the senior citizen cases at a 99% confidence level.