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 1 and for one hour using machine 2, with the following results:

Let's defineas the mean production amount per hour with machine 1 andas the mean production amount per hour with machine 2.

a. National Paper Company wants to know whether the mean production amount per hour differ between Machine 1 and 2? Set up the null and alternative hypotheses.

b. What is the value of the test statistic? (4 decimals) t=

c.Determine the critical value rejection rule. Reject H0 if

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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 randome selected machine operators produce boxes for one hour using machine 1 and for one hour using machine 2, with the following results: Let's dene \"1 as the mean production amount per hour with machine 1 and #2 as the mean production amount per hour with machine 2. a. National Paper Company wants to know whether the mean production amount per hour differ between Machine 1 and 2? Set up the null and altemative hypotheses. HO: #1 - #2 = U Haiti-#2 , '0 b. What is the value of the test statistic? (4 decimals) t= c. Determine the critical value rejection nIIe. Reject HU if t > t alphaiz orI