b) A machine fills cans with soft drinks so that their contents have a volume of 330ml. Over a period of time, it has been established that the volume of liquid in the cans follow a normal distribution with mean of 335 ml and standard deviation of 3 ml. A setting on the machine is altered, following which the operator suspects that the mean volume of liquid discharged by the machine into the cans has decreased. He takes a random sample of 50 cans and finds that the mean volume of liquid in these cans is 344.6 ml. Does this confirm his suspicion? Test at the 5% level of significance. [
b) A random variable of 7 independent observations of a normal variable gave ? ???? = 35. 9 ? ???? 2 = 186.19 Calculate
i. The sample mean [1
] ii. The sample variance [2]
iii. A 90% confidence interval for the population mean