A direct sales company has a large sales force that visits customers. To improve sales, it designs a new training program. To see if the program works, it puts some new employees through this program and others through the standard training. It then assigns two salespeople to a district, one trained in the standard way and the other by the new program. Assume that salespeople trained using the new method sell on average $52,000 per month and those trained by the old method sell on average $45,000 per month. The standard deviation of both amounts is $6,000.
(a) If the dollar amounts sold by the two representatives in a district are independent, then do you expect the salesperson trained by the new program to sell more than the salesperson trained by the old program?
(b) Because the sales representatives operate in the same district, the company hopes that the sales will be positively correlated. Explain why the company prefers positive dependence using an example with r = 0.8.