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 $(25\%,50\%,75\%,or100\%)$and whether the discount was stated precisely (as in, for example, $“60\%$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) Describe a completely randomized design using $200$student subjects. (b) Explain how you would use the partial table of random digits below to assign subjects to treatment groups. Then use your method to select the first $3$subjects for one of the treatment groups. Show your work clearly on your paper.

(c) The figure below 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

a). An equal number of subjects should be in each treatment group.

b). The subjects $20,180$and $193$were selected for treatment.

c). The score seems 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

A study of the attractiveness of advertised price discounts had two factors: percent of all foods on sale $(25\%,50\%,75\%,or100\%)$.

Part (a) Step 2: Explanation

In the question, there are $4$percent of all foods on sale and $2$percent of discount. Each treatment is then a unique combination of one percent of each group. Like we have,

Treatment $1:25\%$of food on sale, $60\%$off

Treatment $2:25\%$of food on sale, $40-70\%$off

Treatment $3:50\%$of food on sale, $60\%$off

Treatment $4:50\%$of food on sale, $40-70\%$off

Treatment $5:75\%$of food on sale, $60\%$off

Treatment $6:75\%$of food on sale, $40-70\%$off

Treatment $7:100\%$of food on sale, $60\%$off

Treatment $8:100\%$of food on sale, $40-70\%$off

An equal number of subjects should be in each treatment group. Thus, given each subject a unique number between $1$ and $200$. A possible simulation then draws randomly a three-digit number. If the number is between $001$ and $200$ then select the corresponding subject for the treatment else ignore the number and move on to the next three-digit number.

Part (b) Step 1: Given Information

The partial table of random digits below assigns subjects to treatment groups.

Part (b) Step 2: Explanation

Work clearly on paper:

$457\Rightarrow \text{Ignore}$

$404⟹\text{Ignore}$

$180⟹\text{Ignore}$

$765⟹\text{Ignore}$

$561⟹\text{Ignore}$

$333⟹\text{Ignore}$

$020\Rightarrow \text{Select subject}020$

$705\Rightarrow \text{Ignore}$

$193\Rightarrow \text{Select subject}193$

Thus, the subjects $20,180$and $193$were selected for treatment.

Part (c) Step 1: Given Information

Percent on sale and precise discount versus range of discounts influence the attractiveness of a sale:

Part (c) Step 2: Explanation

There are $4$ percent of all foods on sale and $2$ percent of discount. Each treatment is then a unique combination of one percent of each group. Thus, a careful description of how percent on sale and precise discount versus range of discounts influence the attractiveness of a sale will be as that the mean score increases strongly as the percent of good on sale increase if the percent is precise. We note that the mean score decreases slightly as the percent of good on sale increase if the percent is a range. Thus, the score seems to be highest for a high percent of goods on sale with a precise percent.