A dentist wants to see if her patients are waiting in the waiting room on average longer than 15 minutes. She takes a random sample of 75 patients and records how many minutes each person spent in the waiting room. She finds the mean waiting time is 16 minutes with a standard deviation of 3 minutes. Is this value significantly greater than 15? Use a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value