Giant Eagle, a grocery store at Pittsburgh, PA is testing out the following "shopper marketing" strategy: When a customer enters the store, he/she will be given a coupon for a certain product category at the back of the store. The hope is to by providing a promotional coupon, the shopper will travel longer in the store, and pick up more unplanned purchases.

The following experimental design is used to test the effectiveness of this strategy on raising unplanned spending. 200 shoppers are intercepted at the entrance of a store. They are randomly divided into two groups: a "treatment" group of 100 shoppers and a "control" group of 100 shoppers. Before they begin their shopping trip, each shopper records all product categories that they plan to buy. The treatment group is given a coupon for a certain product category at the back of the store. The control group is not given a coupon. Both groups are given $5 cash as compensation at the end of their shopping trip.

After their trip ends, an RA gathers the receipt from each shopper and compares it with the shopper's "planned" list to compute the amount that the shopper spent on unplanned purchases, the dependent variable of interest. After analyzing the data, it is revealed that 35 out of 100 shoppers in the "treatment" condition did not redeem the promotional coupon. We define the following groups:

Group C: 100 shoppers in the control group

Group T1: 65 shoppers in the treatment group who redeemed the coupon

Group T2: 35 shoppers in the treatment group who did not redeem the coupon

The retailer wants to compare Group C with Group T1. Is this valid? Why? How should this experimental data be analyzed? Explain.