In industrial settings, alternative methods often exist for measuring variables of interest. The data in Measurement (coded to maintain confidentiality) represent measurements in-line that were collected from an analyzer during the production process and from an analytical lab. (Data extracted from M. Leitnaker, "Comparing Measurement Processes: In-line Versus Analytical Measurements," Quality Engineering, 13, 2000-2001, pp. 293-298.)
a. At the 0.05 level of significance, is there evidence of a difference in the mean measurements in-line and from an analytical lab?
b. What assumption is necessary about the population distribution in order to perform this test?
c. Use a graphical method to evaluate the validity of the assumption in (a).
d. Construct and interpret a 95% confidence interval estimate of the difference in the mean measurements in-line and from an analytical lab.