Chapter 9, Problem 33PS

One operation of a steel mill is to cut pieces of steel info parts that are used in the frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts must be cut to be within $\pm 0.005$ inch of the length specified by the automobile company. The file Steel contains a sample of 100 steel parts. The file steel contains a sample of 100 steel parts. The measurement reported is the difference, in inches, between the actual length of the steel part, a measured by a laser measurement device, and the specified length of the steel part. For example, a value of –0.002 represents a steel shorter than the specified length.

a. At the 0.005 level of significance, is there evidence that the mean difference is different from 0.0 inches?

b. Construct a $95\%$ confidence interval estimate of the population mean. Interpret this interval.

c. Compare the conclusions reached in (a) and (b).

d. Because $n=100,$ do you have to be concerned about the normally assumption needed for

the t test and t interval?