Question 3 (a) In a recent survey of 75 housewives, the average number of hours per week they watched television was 28 with a standard deviation of 3 hours. (i) Find the best point estimate of the population mean. (2 marks) (ii) Find the 99% confidence interval of the mean number of hours watched by all housewives. (5 marks) (b) The owner of a pet shop wanted to estimate the average number of fish his customers purchased. In a sample of 20 customers, he found that they purchased an average of 10 fish, with a standard deviation of 2 fish. Estimate the mean of the population with 95% confidence. (5 marks) (c) A nutritionist wants to estimate the mean amount of cholesterol in a certain variety of chicken eggs. She wants to be within 14 mg. with 99% confidence. It is believed that the population standard deviation is 25 mg. How large a sample of eggs should she use? (5 marks) (d) A random sample of 200 five-year-old children found that 185 believed in Santa Claus. (i) Find p and q, where p is the proportion of of five-year-olds who believe in Santa Claus. (3 marks) (ii) What is the 90% confidence interval for the true proportion of five-year- olds that believe in Santa Claus? (5 marks) [Total : 25 Marks]