Chapter 4: Q AP1.16. (page 279)

Those who advocate for monetary incentives in a work environment claim that this type of incentive has the greatest appeal because it allows the winners to do what they want with their winnings. Those in favor of tangible incentives argue that money lacks the emotional appeal of, say, a weekend for two at a romantic country inn or elegant hotel or a weeklong trip to Europe. A few years ago a national tire company, in an effort to improve sales of a new line of tires, decided to test which method—offering cash incentives or offering non-cash prizes such as vacations—was more successful in increasing
sales. The company had $60$ retail sales districts of various sizes across the country and data on the previous sales volume for each district.
(a) Describe a completely randomized design using the $60$ retail sales districts that would help answer this question.
(b) Explain how you would use the table of random digits below to do the randomization that your design requires. Then use your method to assign treatments to the first $3$ experimental units. Show your work clearly.
$07511 88915 41267 16853 84569 79367 32337 03316 81486 69487 60513 09297 00412 71238 27649 39950$
(c) One of the company’s officers suggested that it would be better to use a matched pairs design instead of a completely randomized design. Explain how you would change your design to accomplish this.

Short Answer

Expert verified

Part (a) The change in sales of each of the selected $30$ groups over time and conduct a comparison of the $30$ groups.

Part (b) The states having numbers $07, 51$ and $18$ are chosen.

Part (c) To see how things have changed, compare the results inside each pair.

Step by step solution

Part (a) Step 1: Given information

The numbers are: $07511 88915 41267 16853 84569 79367 32337 03316 81486 69487 60513 09297 00412 71238 27649 39950$

Part (a) Step 2: Concept

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

Part (a) Step 3: Explanation

Assign the numbers $01$ to $60$ to the $60$ districts presented. Now, select roughly $30$ digits from a random digit number table and assign the monetary incentives to $30$ districts. Observe the change in sales of each of the selected $30$ groups over time and conduct a comparison of the $30$ groups.

Part (b) Step 1: Explanation

Choose the first two digits and choose the districts if the numbers are between $01$ and $60$ ; otherwise, ignore the districts and repeat the process.

Repeat the process until three retail state districts have been selected.

$2 -$ digit number Selected retail sales district

$07$ Select retail sales district $07$

$51$ Select retail sales district $51$

$18$ Select retail sales district $18$

The states with the digits $07, 51,$ and $18$ have been selected.

Part (c) Step 1: Explanation

Choose the two states with the highest sales, as well as the other districts with the highest sales. Flip a coin to choose the district. Assign the incentive to the state if the head comes up. Continue this approach and compare the results inside each pair to see how things have changed.