General stats question

Question 3 (35 Points): The director of quality at a large HMO wants to evaluate the patient waiting times at a local facility. She wants to estimate the mean waiting time within a margin of error of 5 minutes using a 95% confidence interval. An a priori guess of the range of waiting times is 0 to 60 minutes.

a) For an a priori guess of   she used 15 minutes. Explain how she got this guess of   . (5 pts.)
b) Calculate the sample size required to estimate the mean waiting time within a margin of error of 5 minutes using a 95% confidence interval. (5 pts.)
c) A random sample of 36 patients was selected from the appointment book, and their waiting times are given in the file Wait_Time.xls.Calculate a 95% t-interval for the mean waiting time. What is the actual margin of error for this interval? (5 pts.)
d) The goal of the HMO is to have no more than 20% of all the patients to have to wait more than 30 minutes. A consumer group claimed that this sample shows that the HMO is not meeting its goal, and the percentage of all patients having to wait more than 30 minutes is in excess of 20%. Set up the hypotheses to test the consumer group's claim. (5 pts.)
e) Do the data support the consumer group's claim? Find the proportion of patients in the sample who had to wait in excess of 30 minutes. Is this proportion significantly greater than 20% at the 5% significance level? Give the exact P-value of the test statistic and the normal approximation to it. (15 pts.)

Attached file(s):

question3.zip  View File