Question 1: A neighbourhood medical centre initiates a study to evaluate the wait time. The records of 18 randomly selected patients seen since the new procedures were put in place are checked, and the time between entering the emergency department and being seen by urgent care personnel was observed. The mean wait time was 17.82 minutes with a standard deviation of 5.68 minutes. Estimate the mean wait time using a 99% confidence interval. Assume that wait times are normally distributed.
Question 2: The city's Transit Commission wants to determine if there is a need for a change in the frequency of service over certain bus routes. It is determined that the average number of miles traveled by bus over the routes in question by all residents in a given area is about 6.8 per day. If the average number of miles traveled per person differs from 6.8 miles per day then changes in service may be necessary. Use a level of significance of alpha =.05.
A random sample of 145 bus riders is taken and it is found that the sample mean is 5.9 miles per resident per day with a standard deviation is 3.7 miles. Is a change in service necessary?