A department store sampled the purchase amounts (in dollars) of 50 customers during a recent Saturday sale. Half of the customers in the sample used coupons, and the other half did not. The data...

A department store sampled the purchase amounts (in dollars) of 50 customers during a recent Saturday sale. Half of the customers in the sample used coupons, and the other half did not. The data identify the group using a variable coded as
 for those who did not use a coupon and
for those who did use a coupon. The plot at the top of the next page shows the data along with the least squares regression line.

(a) Interpret the estimated intercept, slope, and value of
.

(b) Should managers conclude that customers who use coupons spend statistically significantly more than those who do not?

(c) Suppose the comparison had been done using a pooled two-sample
-test. What would be the value of the
-statistic?

(d) Suppose the comparison had been done using a dummy variable (coded as 1 for coupon users and 0 otherwise) rather than the variable Coupon Status. Give the values of
, and the t-statistic for the estimated slope.