National paper Company must 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. Therefore National paper has decided to compare the machines using a paired difference experiment. Suppose that eight randomly selected machine operators produce boxes for one hour using machine I and for one hour using machine 21 with the following results:

a. Assuming normality, perform a hypothesis test to determine whether there is a difference between the mean hourly outputs of the two machines. Use α = .05.
b. Estimate the minimum and maximum differences between the mean outputs of the two machines. Justify your answer.

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Machine Operator Machine 1 Machine 2 50 55 56 44 450 5747 53 60 58 48 46 54 62 49