Let X equal the thickness of spearmint gum manufactured for vending ma- chines. assume that the distribution of X is N (u, 02). The target thickness is 7.5 hundredths of an inch. We shall test the nul hypothesis Ho : M = 7.5 against a two-sided alternative hypothesis, using 10 observations. field F. (i) Define the test statistic and critical region for an a = 0.05. sketch a figure illustrating this critical region. (5 marks) (ii) Calculate the value of the test statistic and state your decision clearly, using the following n = 10 thicknesses in hundredths of an inch for pieces of gum that were selected randomly from the production line: 7.65, 7.60, 7.65, 7.70, 7.55, 7.55, 7.40, 7.40.7.50, 7.50 (5 marks) (iii) Is u = 7.50 contained in a 95% confidence interval for u? (5 marks) Total: 15 marks