Question

Stores advertise price reductions to attract customers. What type of price cut is most attractive? Experiments with more than one factor allow insight into interactions between the factors. A study of the attractiveness of advertised price discounts had two factors: percent of all foods on sale ($25\%,50\%,75\%,100\%$) and whether the discount was stated precisely (e.g., as in “$60\%$off”) or as a range (as in “$40\%to70\%$off”). Subjects rated the attractiveness of the sale on a scale of $1to7$.

a. List the treatments for this experiment, assuming researchers will use all combinations of the two factors.

b. Describe how you would randomly assign $200$volunteer subjects to treatments.

c. Explain the purpose of the random assignment in part (b).

d. The figure shows the mean ratings for the eight treatments formed from the two factors. Based on these results, write a careful description of how percent on sale and precise discount versus range of discounts influence the attractiveness of a sale.

Short answer

Part a.

Following is the list of treatments:

T1: $25\%$of food on sale, $60\%$off

T2: $25\%$of food on sale, $40\%-70\%$off

T3: $50\%$of food on sale, $60\%$off

T4: $50\%$of food on sale, $40\%-70\%$off

T5: $75\%$of food on sale, $60\%$off

T6: $75\%$of food on sale, $40\%-70\%$off

T7: $100\%$of food on sale, $60\%$off

T8: $100\%$of food on sale, $40\%-70\%$off

Part b. By using any simulation need to draw randomly a $3$-digit number.

Part c. We can conclude that the differences among the different treatment groups.

Part d. The score observed to be highest for a high percent of goods on sale with a precise percent.

Step-by-step solution

Part a. Step 1. Given information

The researcher will use all combinations of the two factors.

Part a. Step 2. Explanation

Following is the list of treatments:

T1: $25\%$of food on sale, $60\%$off

T2: $25\%$of food on sale, $40\%-70\%$off

T3: $50\%$of food on sale, $60\%$off

T4: $50\%$of food on sale, $40\%-70\%$off

T5: $75\%$of food on sale, $60\%$off

T6: $75\%$of food on sale, $40\%-70\%$off

T7: $100\%$of food on sale, $60\%$off

T8: $100\%$of food on sale, $40\%-70\%$ off

Part b. Step 1. Given information

The researcher will use all combinations of the two factors.

Following is the list of treatments:

T1: $25\%$of food on sale, $60\%$off

T2: $25\%$of food on sale, $40\%-70\%$off

T3: $50\%$of food on sale, $60\%$off

T4: $50\%$of food on sale, $40\%-70\%$off

T5: $75\%$of food on sale, $60\%$off

T6: $75\%$of food on sale, $40\%-70\%$off

T7: $100\%$of food on sale, $60\%$off

T8: $100\%$of food on sale, $40\%-70\%$off

Part b. Step 2. Explanation

First need to assign each subject a unique code between $1to200$. Therefore, by using any simulation need to draw randomly a $3$-digit number. After drawing a number, select a corresponding subject for the treatment and then move on to the next $3$-digit number. Using this procedure we can assign all the volunteer subjects to the treatments.

Part c. Step 1. Explanation

There are some reasons behind the random assignment. We randomly assign the subjects to a treatment group such that the different treatment groups are as similar as possible prior to the treatments. To avoid the wrong conclusion, we need to assign subjects randomly to the treatments. We can conclude that the differences among the different treatment groups.

Part d. Step 1. Explanation

There is mean score of sale increases when percent of good on sale increases if the percent if precise. Also, we observed that the mean score decreases slightly as the percent of good on sale increase if the percent is a range. And finally, the score observed to be highest for a high percent of goods on sale with a precise percent.