8.15 A bus company claims that the mean journey time for the service from Paglashonny to Gorley is 53 minutes. A random sample of 35 journeys was chosen and each journey timed. The mean journey time of these journeys was 57 minutes with a standard deviation of 4.6 minutes.

(a) Test the bus company’s claim at the 5 per cent level of significance and comment on the result.

(b) It appears that for nine of these journeys the regular driver was absent from work through illness and relief drivers, who were unfamiliar with the route, had to be used. The mean journey time for the remaining journeys was 55 minutes with a standard deviation of 3.1 minutes. Test the bus company’s claim again at the 5 per cent level of significance using these figures and comment on the result.

(c) What do you need to assume about the population of journey times for the results from the second test to be valid?