Question

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:

Machine 1	Machine 2
53	50
60	55
58	56
48	44
46	45
54	50
62	57
49	47

Let's define μ1μ1 as the mean production amount per hour with machine 1 and μ2μ2 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 alternative hypotheses.

H0: μ1μ1 - μ2μ2 (Click to select)<>=≠≤≥ 0

Ha: μ1μ1 - μ2μ2 (Click to select)=><≥≤≠ 0

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

c. Determine the critical value rejection rule. Reject H0 if (Click to select)t > t alphat <- t alphat > t alpha/2 or t <-t alpha/2d

d. What is the conclusion? (Step 7 of the hypothesis test.)

With 95% confidence we (Click to select)cannotcan conclude that the mean production amount per hour differ between Machine 1 and 2.

e. What is the 99% confidence interval for μ1μ1 - μ2μ2?

______ ≤ μ1μ1 - μ2μ2 ≤ _______

Answer 1

a)

H0: μ1 =μ2

Ha:μ1 μ2

b)

value of the test statistic =6.1775

c) Reject H0 if t>2.3646 or t<-2.3646

d)

reject Ho

e)] With 95% confidence we can conclude that the mean production amount per hour differ between Machine 1 and 2.

f)

99% confidence interval 1.409 to 5.091