Many businesses use some type of customer loyalty program to encourage repeat customers. A common example is the buy-ten-get-one-free punch card. Drèze and Nunes (2006) examined a simple variation of this program that appears to give customers a head start on completing their cards. One group of customers at a car wash was given a buy-eight-get-one-free card and a second group was given a buy-ten-get-one-free card that had already been punched twice. Although both groups needed eight punches to earn a free wash, the group with the two free punches appeared to be closer to reaching their goal. A few months later, the researchers recorded the number of customers who had completed their cards and earned their free car wash.

The following data are similar to the results obtained in the study. Do the data indicate a significant difference between the two card programs? Test with a 5 .05.

Completed Not Completed Buy-Eight-GetOne-Free 10 40 50 Buy-Ten (with 2 Free Punches)

19 31 50 29 71