Exercises 11.89 through 11.92 use the PPROMO data set shown in Table 11.7.

Question 11.89

11.89 Discount promotions at a supermarket.

How does the frequency that a supermarket product is promoted at a discount affect the price that customers expect to pay for the product? Does the percent reduction also affect this expectation? These questions were examined by researchers in a study that used 160 subjects. The treatment conditions corresponded to the number of promotions (one, three, five, or seven) that were described during a 10-week period and the percent that the product was discounted (10%, 20%, 30%, and 40%). Ten students were randomly assigned to each of the treatments.20

ppromo

Table 11.19: TABLE 11.7 Expected price data
Number of
promotions		 Percent
discount		 Expected price ($)
1 40 4.10 4.50 4.47 4.42 4.56 4.69 4.42 4.17 4.31 4.59
1 30 3.57 3.77 3.90 4.49 4.00 4.66 4.48 4.64 4.31 4.43
1 20 4.94 4.59 4.58 4.48 4.55 4.53 4.59 4.66 4.73 5.24
1 10 5.19 4.88 4.78 4.89 4.69 4.96 5.00 4.93 5.10 4.78
3 40 4.07 4.13 4.25 4.23 4.57 4.33 4.17 4.47 4.60 4.02
3 30 4.20 3.94 4.20 3.88 4.35 3.99 4.01 4.22 3.70 4.48
3 20 4.88 4.80 4.46 4.73 3.96 4.42 4.30 4.68 4.45 4.56
3 10 4.90 5.15 4.68 4.98 4.66 4.46 4.70 4.37 4.69 4.97
5 40 3.89 4.18 3.82 4.09 3.94 4.41 4.14 4.15 4.06 3.90
5 30 3.90 3.77 3.86 4.10 4.10 3.81 3.97 3.67 4.05 3.67
5 20 4.11 4.35 4.17 4.11 4.02 4.41 4.48 3.76 4.66 4.44
5 10 4.31 4.36 4.75 4.62 3.74 4.34 4.52 4.37 4.40 4.52
7 40 3.56 3.91 4.05 3.91 4.11 3.61 3.72 3.69 3.79 3.45
7 30 3.45 4.06 3.35 3.67 3.74 3.80 3.90 4.08 3.52 4.03
7 20 3.89 4.45 3.80 4.15 4.41 3.75 3.98 4.07 4.21 4.23
7 10 4.04 4.22 4.39 3.89 4.26 4.41 4.39 4.52 3.87 4.70

586

  1. Plot the expected price versus the number of promotions. Do the same for expected price versus discount. Summarize the results.
  2. These data come from a designed experiment with an equal number of observations for each promotion by discount combination. Find the means and standard deviations for expected price for each of these combinations. Describe any patterns that are evident in these summaries.
  3. Using your summaries from part (b), make a plot of the mean expected price versus the number of promotions for the 10% discount condition. Connect these means with straight lines. On the same plot, add the means for the other discount conditions. Summarize the major features of this plot.

11.89

(a) As the number of promotions increases, the expected price goes down. For discount, the expected price for 10% and 20% seem similar, as does the expected price for 30% and 40%, which is lower than the expected price for 10% and 20%. (b) and (c) The drop of expected price is fairly consistent with an increase in promotions. Similarly, the drop in price is fairly consistent with increase percent discount; however, the 40% discount consistently yields higher expected prices than when the 30% discount is used.

Promotions Discount Mean Std Dev
1 10 4.92 0.1520234
20 4.689 0.2330689
30 4.225 0.3856092
40 4.423 0.1847551
3 10 4.756 0.2429083
20 4.524 0.2707274
30 4.097 0.2346179
40 4.284 0.2040261
5 10 4.393 0.2685372
20 4.251 0.2648459
30 3.89 0.1628906
40 4.058 0.1759924
7 10 4.269 0.2699156
20 4.094 0.2407488
30 3.76 0.2617887
40 3.78 0.2143725