The data for a sample of

80

steel parts, given in the accompanying table, show the reported difference, in inches, between the actual length of the steel part and the specified length of the steel part. For example, a value of

0.002

represents a steel part that is 0.002 inch shorter than the specified length. Complete parts (a) through (d).

0.001

0.0015

0.003

0.0025

0.003

-0.0025

0.0005

0.001

0.0005

0.002

-0.0005

-0.001

-0.0005

0.0005

0.003

0.0015

0.002

-0.0025

0.003

0.0025

0.0025

-0.0005

0

0.003

-0.0005

0.003

-0.001

-0.0025

-0.0025

0.0005

-0.0015

0.0005

0.003

-0.001

-0.0005

0.002

0.0015

-0.001

0.003

-0.001

0.0005

0.002

-0.0005

-0.003

0.001

0.0025

0.0005

0.001

-0.002

0.001

0.003

0.001

0.002

-0.0015

-0.002

-0.001

-0.002

0.0005

0.0025

-0.002

-0.0005

-0.001

-0.002

-0.002

0.001

0.0005

-0.0005

0.001

-0.002

-0.003

-0.002

0.0015

-0.003

0.0025

-0.0025

-0.002

0.0005

-0.001

0.001

-0.001

a. At the 0.20 level of significance, is there evidence that the mean difference is different from 0.0 inches?State the null and alternative hypotheses. evidence to conclude that the mean difference is not equal to 0.0 inches.

Part 5b. Construct a

80%

confidence interval estimate of the population mean.

enter your response hereenter your response here

Part 6c. Compare the conclusions reached in (a) and (b). Choose the correct answer below.

A.

The confidence interval shows sufficient evidence while the hypothesis test shows insufficient evidence to support the claim that the mean difference is not equal to

0.0

inches.

B.

The confidence interval and hypothesis test both show that there is

sufficient

evidence to support the claim that the mean difference is not equal to

0.0

inches.

C.

The confidence interval shows insufficient evidence while the hypothesis test shows sufficient evidence to support the claim that the mean difference is not equal to

0.0

inches.

D.

The confidence interval and hypothesis test both show that there is

insufficient

evidence to support the claim that the mean difference is not equal to

0.0

inches.

Part 7d. Because n=80, do you have to be concerned about the normality assumption needed for the ttest and tinterval?

A.

Yes, because the normality assumption is needed if the hypothesis test shows sufficient evidence that the mean difference is not equal to

0.0

inches.

B.

Yes, because the population distribution must be normal for all sample sizes.

C.

With the large sample size, the

ttest

is still valid unless the population is very skewed.

D.

No, because the normality assumption is needed only if the hypothesis test shows sufficient evidence that the mean difference is not equal to

0.0

inches.