(a) Two post mix beverage machines are adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was taken from Machine A and 17 beverages from Machine B. The syrup content (in fluid ounces) was measured, resulting in the following data: Machine A n, = 25 x, =1.10 S, = 0.015 Machine B n, = 17 X, = 1.07 N'T = 0.017 (i) A researcher claimed that the mean syrup content for Machine A is more than 1.05 ounces. Test at 5% level of significance to prove the claim. (6 marks) (ii) Test Ho : M = /2 versus Ho : M # /2 at a = 0.05. Draw your conclusion. (7 marks) The sample standard deviation of the waiting time (in minutes) from two different hospitals are measured and following is the result: Hospital A n = 9 S1 = 32 Hospital B n, = 8 S , = 28 (i) Construct a 98% confidence interval for population variance, o of Hospital A. (5 marks) (ii) Test at 5% significance level to conclude that the standard deviation of the waiting time in Hospital A is greater than the standard deviation of the waiting time in Hospital B. (7 marks)