Question 15.47

15.47 Discounts and expected prices.

CASE 15.1 Case 15.1 (page 15-15) describes a study designed to determine how the frequency that a supermarket product is promoted at a discount and the size of the discount affect the price that customers expect to pay for the product. In the exercises that followed, we examined the data for two levels of each factor.

Table 15.2 gives the complete set of data.

freqd

  1. Summarize the means and standard deviations in a table and plot the means. Summarize the main features of the plot.
  2. Analyze the data with a two-way ANOVA. Report the results of this analysis.
  3. Using your plot and the ANOVA results, prepare a short report explaining how the expected price depends on the number of promotions and the percent of the discount.
Table 15.40: TABLE 15.2 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

15.47

(a) As promotions increase, expected price goes down. Expected price is also different for different discounts. The expected price from highest to lowest is 10%, 20%, 40%, and 30%. For some reason, the 30% discount gives lower expected prices than the 40% discount. There doesn’t appear to be an interaction effect; only with 7 promotions at the 40% level do we see something unusual happen, where it is much lower than where we might expect it to be.

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

(b) Promotions is very significant, Discount is also very significant, The interaction effect is not significant, (c) As promotions increase, expected price goes down. Expected price is also different for different discounts. The expected price from highest to lowest is 10%, 20%, 40%, and 30%. For some reason the 30% discount gives lower expected prices than the 40% discount.