A Paper Company needs to purchase a new machine for producing cardboard boxes. The company must choose between two machines. The machines produce boxes of equal quality, so the company will choose the machine that produces (on average) the most boxes. It is known that there are substantial differences in the abilities of the company's machine operators who will be operating those machines to produce the cardboard boxes. The company randomly selects 20 operators to produce boxes for one hour using machine 1 and then the same 20 operators produce boxes for one hour using machine 2.

The number of boxes produced by these operators across the two machines is given in the Excel spreadsheet Problem2.xlsx

Perform a hypothesis test to see if the mean hourly output of Machine 1 is greater than that of machine 2.

(a) Clearly state which test you used and give an argument for using that particular test. Also state your Null and alternate hypothesis.

(b) Report the t statistic (t_calculated) and also report the conclusion from your hypothesis test (i.e., report whether the mean hourly output of Machine 1 is greater than that of machine 2.

Machine_Operator	Boxes_produced_from_Machine_1	Boxes_produced_from_Machine_2
1	53	50
2	60	55
3	58	56
4	48	44
5	46	45
6	54	50
7	62	57
8	49	47
9	51	52
10	64	64
11	48	53
12	50	45
13	54	50
14	55	60
15	55	54
16	52	46
17	47	46
18	56	48
19	58	48
20	54	50