(5) [H] Suppose that you are given a random sample (n = 18) of annual salaries for a specific position. The observed sample mean is E = 54, 500$. Assume population is normal with standard deviation or = 9, 500$. (a) (4 marks) Find a 90% confidence interval for the true mean annual salary. (b) (4 marks) How large the sample size is necessary for the margin of error to be at most 3000$? (6) [H] Historical data shows that approximately 64% of Ontario public school principals in one province were female. Recently, a study showed that 231 of 328 randomly selected principals in Ontario were female. (a) (6 marks) Is there any evidence to suggest that the proportion of female principals has changed? Use significance testing with a = 0.05. (b) (3 marks) Find the 99% confidence interval for the true population proportion p. (c) (3 marks) Using the above information as prior experience, find the minimum sample size such that the margin of error is no larger than 0.1 for a 99% confidence interval