The owner of a large car dealership wants to understand the negotiation process for buying a new car. Cars are given a “sticker price,” but a potential buyer may negotiate a better price. The owner wonders if there’s a difference in how men and women negotiate and who, if either, obtains the larger discount. He takes a random sample of 100 customers from the last six months’ sales and finds that 54 were men and 46 were women. On average, the 54 men received a discount of \($962.96\) with a standard deviation of \($458.95;\) the 46 women received an average discount of \($1262.61\) with a standard deviation of \($399.70\).
QUESTION:

What is the mean difference of the discounts received by men and women? What is its standard error?