Question

Price cuts (4.2) 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%, or 100%) and whether the discount was stated precisely (e.g., as in “60% off”) or as a range (as in “40% to 70% off”). Subjects rated the attractiveness of the sale on a scale of 1 to 7.
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.35 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)The researcher will use all combinations of the two factors.

$\mathrm{T}1:25\%$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) First, each subject must be assigned a unique code ranging from 1 to 200. As a result, any simulation must generate a three-digit number at random. After drawing a number, choose a subject for treatment and move on to the next 3-digit number. Using this procedure, we can assign treatments to all of the volunteer subjects.

Part c) There are several reasons for the random assignment. We assign subjects to treatment groups at random so that the groups are as similar as possible prior to the treatments. To avoid reaching the wrong conclusion, we must assign subjects to treatments at random. We can conclude the differences between treatment groups.

Part d) When the percentage of goods on sale increases, the mean score of the sale increases. Also, if the percentage is a range, we found that the mean score decreases slightly as the percentage of goods sold increases. Finally, the highest score was observed for a high percentage of goods on sale with a precise percentage.

Step-by-step solution

Part a) Step 1: The objective is to determine to list the treatment for this experiment

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 1: The objective is to describe how would assign 200 volunteer subjects to treatments. 

First, each subject must be assigned a unique code ranging from 1 to 200. As a result, any simulation must generate a three-digit number at random. After drawing a number, choose a subject for treatment and move on to the next 3-digit number. Using this procedure, we can assign treatments to all of the volunteer subjects.

Part c) Step 1: The obh=jective is to explain the purpose of random assignment

There are several reasons for the random assignment. We assign subjects to treatment groups at random so that the groups are as similar as possible prior to the treatments. To avoid reaching the wrong conclusion, we must assign subjects to treatments at random. We can conclude the differences between treatment groups.

Part d) Step 1: The objective is to explain the description of how the percent on sale and precise discount versus the range of discounts influence the attractiveness of the sale.

When the percentage of goods on sale increases, the mean score of the sale increases. Also, if the percentage is a range, we found that the mean score decreases slightly as the percentage of goods sold increases. Finally, the highest score was observed for a high percentage of goods on sale with a precise percentage.