PROBLEM 4 (25 points)

The Medical Rehabilitation Foundation reports that the average cost of rehabilitation for stroke victims is at least $24,500. To see if the average cost might be different at a particular hospital, a researcher selects a random number sample of 50 stroke victims and finds that the average cost is $25,225. The standard deviation of the population is $1,300. 

a) At α = .01, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is at least $24,500?  

b) Construct a 90% confidence interval