One operation of a steel mill is to cut pieces of steel into 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 +/-0.005 inch of the length specified by the automobile company. 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, as measured by a laser measurement device, 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.
a. At the 0.05 level of significance, is there evidence that the mean difference is not equal to 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 normality assumption needed for the t test and t interval?