Members of a sales force were randomly assigned to two management groups. Each group employed a different technique for motivating and supporting the sales team. Let’s label these groups A and B, and...

Members of a sales force were randomly assigned to two management groups. Each group employed a different technique for motivating and supporting the sales team. Let’s label these groups A and B, and let
 denote the mean weekly sales generated by members of the two groups. The 95% confidence interval for
 was found to be [$500, $2,200].

(a) If profits are 40% of sales, what’s the 95% confidence interval for the difference in profits generated by the two methods?

(b) Assuming the usual conditions, should we conclude that the approach taken by Group A sells more than that taken by Group B, or can we dismiss the observed difference as due to chance?

(c) The manager responsible for Group B complained that his group had been assigned the “poor performers” and that the results were not his fault. How would you respond?