One operation of a 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 the resulting parts must be cut to be within+/- 0.005 inch of the length specified by the automobile company. The measurement reported from a sample of 100 steel parts (stored in Steel) 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, the first observation, -0.002 represents a steel part that is 0.002 inch shorter than the specified length.
a. Construct a 95% confidence interval estimate for the population mean difference between the actual length of the steel part and the specified length of the steel part.
b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?
Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.