Questions 11 - 15 Write Your Answers In Space Provided Question 11 (3 + 5 = 8 marks) (a) A retail chain CEO wants to estimate the proportion of employees who are within five years of retirement. How large a sample is needed if he wants to be within 3% of the population proportion with 90% confidence? (b) Aclaim is published that in a certain area of high unemployment, $195 is the average amount spent on food per week by a family of four. A home economist wants to test this claim against the suspicion that the true average is lower than $195. She surveys a random sample of 16 families from the locality and finds the mean to be $193.20 with a standard deviation of $2.80. Can we conclude that the home economist's suspicions are correct? Use a 1% level of significance