The owner of a gas station wants to study gasoline purchasing habits of motorists at his station. He selects a random sample of 60 motorists during a certain week, with the following results:

The average amount purchased = 42.78 litres

Standard Deviation = 11.73 litres

11 motorists purchased premium-grade gasoline

a) At the 0.05 level of significance, is there evidence that the mean amount purchased was differed significantly from 38 litres? (show all work).

b) Determine the p-value in (a). (show all work).

c) At the 0.05 level of significance, is there evidence that fewer than 20% of all the motorists at the station purchased premium-grade gasoline? (show all work).

d) What is your answer to (a) if the sample mean equals 40 litres?