A high street chemist has installed new stock control system

A high street chemist has installed new stock control system to expedite the delivery of prescription medicines to its customers. Prior to the installation of this system the mean time interval between customers presenting prescriptions and the medicine being dispensed to them was 15.8 minutes. Since the introduction of the new system the manager measure the time taken to dispense prescriptions to a random sample of 41 customers was 14.6 minutes with a standard deviation of 5.3 minutes.

a) Test the hypothesis that the new stock control system has resulted in a faster average dispensing time using a 5% level of significance.

b) Later I emerges that 25 of the prescriptions out of the sample of 41 were dispense by an employee who had received no training in the use of the system. If these results are removed the mean and standard deviation of the dispensing times of the remaining prescriptions were 13.1 and 4.6 respectively. Test the hypothesis that the new stock control system has yielded a faster average dispensing time using these sample results and a 5% level of significance.

c) Contrast the results of the two tests and identify the assumption that must be made for the second test to be valid.

Solution