Question: Peter S. Kastner, director of the consulting firm Vericours Inc., reported that 40% of all rebates are not redeemed because consumers either fail to apply for them or their applications are rejected. TCA Fulfillment Services published its redemption rates: 50% for a $30 rebate on a $100 product, 10% for a $10 rebate on a $100 product, and 35% for a $50 rebate on a $200 product.
a. Calculate the weighted average proportion of redemption rates for TCA Fulfillment using the size of the rebate to establish the weights. Does it appear that TCA Fulfillment has a lower rebate rate than that indicated by Vericours? Explain.
b. To more accurately answer the question posed in part a, a random sample of 20 individuals who purchased an item accompanied by a rebate could be asked if they submitted their rebate. Suppose four of the questioned individuals said they did redeem their rebate. If Vericours' estimate of the redemption rate is correct, determine the expected number of rebates that would be redeemed. Does it appear that Vericours' estimate may be too high?
c. Determine the likelihood that such an extreme sample result as indicated in part b or something more extreme would occur if the weighted average proportion provides the actual rebate rate.
d. Repeat the calculations of part c assuming that Vericours' estimate of the redemption rate is correct. e. Are you convinced that the redemption rate is smaller than that indicated by Vericours? Explain.