ANSWER ALL 4 QUESTIONS

Question 4 (40 points) (a) Outline the general steps taken in a parametric statistical hypothesis test using a two-sided test for a population mean to illustrate each step. (b) Describe what is meant by Type I and Type II errors in hypothesis testing and explain how the probabilities of these errors are related to each other, and to the significance level of the test. Illustrate your answer with a dia- gram. (c) It is stated in a consumer magazine that the average price of football shirts in London is 29.00. A random sample is taken by obtaining a single football shirt from each of 26 randomly chosen London retailers. The sample mean is 232 and the sample standard deviation is 28.40. Carry out a hypothesis test, at 5% significance level, to determine whether the price of football shirts in London is more expensive than the price stated in the consumer magazine. State your hypothesis, the test statistic and its distribution under the null hypothesis, and your conclusion in the context of the problem. (d) Find the highest probability level such that the null hypothesis is rejected