Q5 A company plans to purchase a machine for producing plastic chair. They have two options: machine A and machine B. The machines produce chairs of equal quality, the company will choose the machine which produces the chair faster. It is known that the machine operator has substantial effect on the speed. Hence the company randomly chooses 5 operators, each operator produces chairs using machine A and machine B, both for one-hour. The number of produced chairs are listed below.

Machine A 5 4 7 4 6

Machine B 3 4 5 3 5

machine A 4 7 4 machine B 3

Let uA, uB be the average number of chairs produced by two machines in one hour, respectively. Assume normality.

1. Implement the hypothesis test if the machine A is faster than B. Solve using reject region method. Significance level is 0.05.

2 Calculate 99%(two-sided) confidence interval for the mean difference : uA- uB-