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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鈥攐ffering cash incentives or offering non-cash

Prizes such as vacations鈥攚as 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 following excerpt from the table of random digits to

Do the random assignment that your design requires. Then use your method to make

The first three assignments.

07511	88915	41267	16853	84569	79367	32337	03316
81486	69487	60513	09297	00412	71238	27649	39950

c. One of the company鈥檚 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.

Step by step solution

01

Part (a) Step 1: Given Information

We need to describe the design using retail sales.

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

02

Part (a) Step 2: Explanation

Number of $60$retail sales districts with 2 digit number from $1-60$.Using a table of random Digits , Read $2$digit numbers until $30$unique numbers from $1-60$have been chosen. the corresponding $30$sets are assign in a monetary incentive group.

03

Part (a) Step 1: Given Information

We need to Explain how you would use the following excerpt from the table of random digits to

Do the random assignment that your design requires.

04

Part (b) Step 2: Explanation

We are given that

07511	88915	41267	16853	84569	79367	32337	03316
81486	69487	60513	09297	00412	71238	27649	39950

If the number is between $1-60$, select the first two digit number in the given lines. If so, the appropriate Retail sales district is chosen; otherwise, ignore it. Repeat until three distinct retail sales districts have been chosen.

$2$digit number	Selected retail sales district
$07$	select retail sales district $07$
$51$	select retail sales district $51$
$18$	select retail sales district $18$

Hence we note these retail sales.

05

Part (c) Step 1: Given Information

We need to find the ways to change the design .

06

Part (c) Step 2: Explanation

Pair the two districts with large sales . the next two largest ,down to two small districts. For each Pair, pick one of the district and flip the coin. If the flips is head this districted is assigned to the Cash incentives group. and flip is tails this districted is assigned to the non cash incentives group. The other pair is assigned to other group. record the changes in sales for each district and Compare with each other.

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