An IT manager considers that the average number of hits per week on the company intranet pages should be 75. The mean number of hits per week on a random sample of 38 pages is 71.4 with a standard deviation of 31.9.

(a) Test a suitable hypothesis at the 10% level of significance to assess the plausibility of the IT manager's assertion.

(b) It later emerges that 18 of these pages are often visited by non-company users, and should therefore not be included in the sample. The mean and standard deviation of the remaining 20 pages are 65.8 and 28.3 respectively. Test the same hypothesis again at the 10% level. What assumption must you make for the test to be valid?