Chapter 8.3, Problem 80E

(a)

To determine

To describe a completely randomized design using $200$ student subjects.

Explanation of Solution

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,

  $\begin{array}{l}\text{Treatment 1: 25\% of food on sale, 60\% off}\\ \text{Treatment 2: 25\% of food on sale, 40}-70\text{\% off}\\ \text{Treatment 3: 50\% of food on sale, 60\% off}\\ \text{Treatment 4: 50\% of food on sale, 40}-70\text{\% off}\\ \text{Treatment 5: 75\% of food on sale, 60\% off}\\ \text{Treatment 6: 75\% of food on sale, 40}-70\text{\% off}\\ \text{Treatment 7: 100\% of food on sale, 60\% off}\\ \text{Treatment 8: 100\% of food on sale, 40}-70\text{\% off}\end{array}$

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

(b)

To determine

To explain how you would use a partial table of random digits below to assign subjects to treatment groups.

Explanation of Solution

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,

  $\begin{array}{l}\text{Treatment 1: 25\% of food on sale, 60\% off}\\ \text{Treatment 2: 25\% of food on sale, 40}-70\text{\% off}\\ \text{Treatment 3: 50\% of food on sale, 60\% off}\\ \text{Treatment 4: 50\% of food on sale, 40}-70\text{\% off}\\ \text{Treatment 5: 75\% of food on sale, 60\% off}\\ \text{Treatment 6: 75\% of food on sale, 40}-70\text{\% off}\\ \text{Treatment 7: 100\% of food on sale, 60\% off}\\ \text{Treatment 8: 100\% of food on sale, 40}-70\text{\% off}\end{array}$

An equal number of subjects should be in each treatment group. Thus, given each subject a unique number between $1\text{ and 200}$ . A possible simulation then draws randomly a three-digit number. Thus the list of the random digits is given in the question. Now, if the number is between $001\text{ and 200}$ then select the corresponding subject for the treatment else ignore the number and move on to the next three-digit number. As,

  $\begin{array}{l}457\Rightarrow \text{ Ignore}\\ \text{404}\Rightarrow \text{ Ignore}\\ 180\Rightarrow \text{ Select subject 180}\\ 765\Rightarrow \text{ Ignore}\\ 561\Rightarrow \text{ Ignore}\\ 333\Rightarrow \text{ Ignore}\\ 020\Rightarrow \text{ Select subject }020\\ 705\Rightarrow \text{ Ignore}\\ 193\Rightarrow \text{ Select subject }193\end{array}$

Thus, the subjects $20,180\text{ and 193}$ were selected for treatment.

(c)

To determine

To explain a careful description of how percent on sale and precise discount versus range of discounts influence the attractiveness of a sale.

Explanation of Solution

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. 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.