Many companies now use text messaging on cell phones as a means of marketing their products. One way to do this is to send a redeemable discount coupon (called an m-coupon) via a text. The redemption rate of m-coupons-the proportion of coupons redeemed-was the subject of an article in the Journal of Marketing Research (October 2015). In a two-year study, over 8,000 mall shoppers participated by signing up to receive mcoupons. The researchers were interested in comparing the redemption rates of m-coupons for different products. In a sample of 2,447 m-coupons for products sold at a milkshake store, 79 were redeemed; in a sample of 6,619 m-coupons for products sold at a donut store, 72 were redeemed.
a. Compute the redemption rate for the sample of milkshake m-coupons.
b. Compute the redemption rate for the sample of donut m-coupons.
c. Give a point estimate for the difference between the true redemption rates.
d. Form a 90% confidence interval for the difference between the true redemption rates. Give a practical interpretation of the result.
e. Explain the meaning of the phrase "90% confident" in your answer to part d.
f. Based on the interval, part d, is there a "statistically" significant difference between the redemption rates? (Recall that a result is "statistically" significant if there is evidence to show that the true difference in proportions is not 0.)
g. Assume the true difference between redemption rates must exceed .01 (i.e., 1%) for the researchers to consider the difference to be "practically" significant. Based on the interval, part c, is there a "practically" significant difference between the redemption rates?