A computer systems retailer wishes to compare the average monthly sales of its servers with Intel and AMD multi-core processors. To do so, they record the number of sales of each server type for each of the last 12 months:

Month Intel AMD
Jan 900 840
Feb 720 700
Mar 660 600
Apr 700 680
May 900 840
Jun 860 920
Jul 760 740
Aug 1100 1080
Sep 1380 1280
Oct 920 860
Nov 880 820
Dec 780 780

a) For this dataset, why should the company use a paired difference analysis instead of an independent samples analysis?

b) Compute the 95% confidence interval for the average monthly sales of each server type (μ1, μ2).

c) Compute the 95% confidence interval for the difference in monthly sales μ1 - μ2.

d) Notice that the confidence intervals in part b overlap, but the confidence interval in part c does not contain μ1 - μ2 = 0. describe the discrepancy between these two results. Which result is a better indicator of whether or not μ1 and μ2 are likely to be identical?

e) Is the sample evidence sufficient to conclude whether μ1 and μ2 are different? To answer this problem, perform a hypothesis test at α = .05. You should state the alternative and null hypotheses, compare the observed t-score to the t-score threshold, estimate the p-value, and state the conclusion of the test.