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) examineda 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 secoDnd 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. Completed Not Completed Buy 8 get 1 free 10 40 50 Buy 10 with 2 free 19 31 50 29 71 Do the data indicate a significant difference between the two card programs? Test with a = .05. Find the expected frequencdes and compute the chi-square statistic. (Use two decimal places for fe and y2, three for each (fo- fe)/fe.) Cell fo fe (fo - fe) /fe Buy 8 get 1 free-Completed Buy 8 get 1 free-Not Completed 10 40 Buy 10 with 2 free-Completed Buy 10 with 2 free-Not Completed 31 19 Chi-Square Distribution Degrees of Freedom = 16 0123 45 67 89 101112 1314 15 1617 18 19 20 21 22 2324 25 26 27 28 29 30 x² critical value x² Conclusion: O Reject the null hypothesis; there is no significant difference between the two card programs. O Fail to reject the null hypothesis; there is no significant difference between the two card programs. Reject the null hypothesis; there is a significant difference between the two card programs. .O Fail to reject the null hypothesis; there is a significant difference between the two card programs,