8.22 Incentives to Exercise Exercise 5.29 on page 385 describes a study designed to see what type ofincentive might be most effective in encouraging people to exercise. In the study, 281 overweight orobese people were assigned the goal to walk 700o steps a day, and their activity was tracked for 100days. The response variable is the number of days (out of 100) that each participant met the goal. Theparticipants were randomly assigned to one of four different incentive groups: for each day they met thegoal, participants in the first group got only praise, participants in the second group got entered into alottery, and participants in the third group received cash (about $1.50 per day). In the fourth group,participants received all the money up front and lost money (about $1.50 per day) if they didn't meetthe goal. (The overall financial effect for participants in the third and fourth conditions is identical, butthe psychological effect between winning money and losing money is potentially quite different.) Thesummary statisticsé for the four conditions and overall are shown in Table 8.7.TABLE 8.7.Number of days meetingan exercise goalCondition nMean St.Dev.Praise70 30.032.0Lottery70 35.029.9Get money70 36.029.4Lose money 7145.030.1281 36.5Overall30.6865In exercise 8.22,1. A: Test each pairwise difference between themeans.2. B: Write up: What effects or combinations ofeffects are important., and what it means interms of the problem

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Asked Dec 6, 2019
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8.22 Incentives to Exercise Exercise 5.29 on page 385 describes a study designed to see what type of
incentive might be most effective in encouraging people to exercise. In the study, 281 overweight or
obese people were assigned the goal to walk 700o steps a day, and their activity was tracked for 100
days. The response variable is the number of days (out of 100) that each participant met the goal. The
participants were randomly assigned to one of four different incentive groups: for each day they met the
goal, participants in the first group got only praise, participants in the second group got entered into a
lottery, and participants in the third group received cash (about $1.50 per day). In the fourth group,
participants received all the money up front and lost money (about $1.50 per day) if they didn't meet
the goal. (The overall financial effect for participants in the third and fourth conditions is identical, but
the psychological effect between winning money and losing money is potentially quite different.) The
summary statisticsé for the four conditions and overall are shown in Table 8.7.
TABLE 8.7.
Number of days meeting
an exercise goal
Condition n
Mean St.Dev.
Praise
70 30.0
32.0
Lottery
70 35.0
29.9
Get money
70 36.0
29.4
Lose money 71
45.0
30.1
281 36.5
Overall
30.6865
In exercise 8.22,
1. A: Test each pairwise difference between the
means.
2. B: Write up: What effects or combinations of
effects are important., and what it means in
terms of the problem
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8.22 Incentives to Exercise Exercise 5.29 on page 385 describes a study designed to see what type of incentive might be most effective in encouraging people to exercise. In the study, 281 overweight or obese people were assigned the goal to walk 700o steps a day, and their activity was tracked for 100 days. The response variable is the number of days (out of 100) that each participant met the goal. The participants were randomly assigned to one of four different incentive groups: for each day they met the goal, participants in the first group got only praise, participants in the second group got entered into a lottery, and participants in the third group received cash (about $1.50 per day). In the fourth group, participants received all the money up front and lost money (about $1.50 per day) if they didn't meet the goal. (The overall financial effect for participants in the third and fourth conditions is identical, but the psychological effect between winning money and losing money is potentially quite different.) The summary statisticsé for the four conditions and overall are shown in Table 8.7. TABLE 8.7. Number of days meeting an exercise goal Condition n Mean St.Dev. Praise 70 30.0 32.0 Lottery 70 35.0 29.9 Get money 70 36.0 29.4 Lose money 71 45.0 30.1 281 36.5 Overall 30.6865 In exercise 8.22, 1. A: Test each pairwise difference between the means. 2. B: Write up: What effects or combinations of effects are important., and what it means in terms of the problem

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Expert Answer

Step 1

Given data and calculation is shown below

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Number of days meeting an exercise goal St. Dev Condition Mean Praise 70 30 32 70 Lottery Get Money Lose Money 35 29.9 29.4 70 36 71 45 30.1 Overall 281 36.5 30.6865 SSBetween is given by E, n; (x; – x)2 = 70 × (30 – 36.5)² + 70 × (35 – 36.5)² + 70 × (36 – 36.5)² + SSBetween 71 x (45 – 36.5)² i=1 = 8262. 25 d.o.fBetween = 4 –1= 3 SSBetween d.o. fßetween 8262.25 MSBetween 2754.08 3

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Step 2

calculation continue

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> (n; – 1) x s? SSwithin = i=1 = (70 – 1) x 32² + (70 – 1) × 29.92 + (70 – 1) × 29.4? + (71 – 1) × 30.12 = 255404.2 d.o.fwithin = 281 – 4= 277 SSwithin 255404.2 MSwithin = 922.04 d.o. fwithin 277 Test-statistic is given by MSBetween MSwithin 2754.08 = 2.99 922.04 Considering significance level a = 0.05 Critical value of F is given by Fafbetween df within.0.05 = F3,277,0.05 = 2.64(From Excel = F.INV.RT(0.05,3,277))

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Step 3

p-value is given by

p-value = 0.03(From Excel  =F.DIST.RT(2.99,3,277))

To test each pairwise d...

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MSwithin т Яa(сл-с) пi Where on c and n – c d.o.f qa(c.n-c) = Studentized range distribution, based c = Number of Treatments(i.e no of columns) n = Total Sample size Sample size of the treatment group with the smallest number of observations пi 3.633 Ta(c,n-c) = 90.05(4,281-4) 922.04 T = 3.633 13.185 70

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