Chapter 4, Problem AP1.16CPT

(a)

To determine

To describe a completely randomized design using the sixty retail sales districts that would help answer this question.

Explanation of Solution

Number the $60$ retail sales districts with a two-digit number from $01-60$ . Using a table of random digits, read two-digit numbers until $30$ unique numbers from $01-60$ have been chosen. The corresponding $30$ districts are assigned to the monetary incentives group. After a specified period of time, record the change in sales for each district and compare the two groups.

(b)

To determine

To explain how would you use the following excerpt from the table of random digits to do a random assignment that your design requires.

Explanation of Solution

Given:

  $\begin{array}{l}07511,88915,41267,16853,84569,79367,32337,03316,81486,\\ 69487,60513,09297,00412,71238,27649,39950\\ \text{Number the 60 retail sales districts from 01 to 60}\text{.}\\ \text{Select the first 2-digit number in the given lines}\text{. If the number is between 01 and 60,}\\ \text{then the corresponding retail sales district is selected, else ignore the number and }\\ \text{select the next 2-digit number}\text{.}\\ \text{Repeat until 3 unique retail sales districts are selected}\text{.}\\ \text{07}\Rightarrow \text{Select retail sales district 07}\\ \text{51}\Rightarrow \text{Select retail sales district}51\\ 18\Rightarrow \text{Select retail sales district}18\\ \text{Thus we then note that retail sales districts 07,51 and 18 are selected}\text{.}\end{array}$

(c)

To determine

To explain how would you change your design to accomplish this.

Explanation of Solution

Pair the two districts with the largest sales, the next two largest, down to the two smallest districts. For each pair, pick one of the districts and flip a coin. If the flip is "heads", this district is assigned to the cash incentives group. If the flip is "tails", the district is assigned to the non-cash incentives group.The other pair is assigned to the other group. After a specified period of time, record the change in sales for each district and compare within each pair.