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[solution]: Please show all work step by step using both hand calculations


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Please show all work step by step using both hand calculations and excel.


Part 1 Lab Rats - Investigating red dye #40

 

S.W. Laagakos and F. Mosteller of Harvard University fed 15 mice different doses of red dye

 

number 40 and recorded the time of death in weeks.

 

Reference: Journal Natl. Cancer Inst., Vol. 66, p 197-212

 


 

Results for female mice, dosage and time of death are shown in the data

 

X1 = time of death for control group (normal mice with no dosage)

 

X2 = time of death for group with low dosage

 

X3 = time of death for group with higher dosage

 


 

X1

 


 

X2

 


 

X3

 


 

70

 


 

49

 


 

34

 


 

77

 


 

60

 


 

36

 


 

83

 


 

63

 


 

48

 


 

87

 


 

67

 


 

48

 


 

92

 


 

70

 


 

65

 


 

Is there a difference in the average times of death? Since there are more than 2 populations, use

 

ANOVA to see if we can prove a difference.

 

Answer the following questions:

 

a) What are the 3 populations being studied?

 

b) What are the population parameters? (Define each of them!)

 

c) One of the conditions for using ANOVA is that the population variances are equal. In reality, the

 

one-way ANOVA test is not too sensitive to inequality of variances if the sample sizes are equal -which they are. A rule of thumb: As long one sample variance is no more than 3-times another. Is

 

this true for our problem? Explain.

 

d) Use ANOVA and run a hypothesis test to see if it can be proven that not all the population

 

means are the same. Do this by setting up a null and alternative hypotheses and showing each

 

step by hand using a test statistic / critical value approach. Use alpha = .05

 

e) Run the above test using a p-value / level of significance approach. Click Once for instructions

 

on using Excel to get a p-value:Example ANOVA using Excel -- Include Excel file in Report

 

complete with ANOVA table.

 


 

f) If you were able to determine that there was a difference in the means, use Fisher's LSD to do

 

multiple pairwise tests?

 

g) What is your overall conclusion?

 


 

Part 2 NFL Lightweights- Do some teams weigh less than others?

 

The following data represent weights (pounds) of a random sample of professional football

 

players on the following teams.

 


 

Fort

 

Cowbo Packe

 

y

 

ys

 

rs

 

Nine

 

rs

 

250

 


 

260

 


 

247

 


 

255

 


 

271

 


 

249

 


 

255

 


 

258

 


 

255

 


 

264

 


 

263

 


 

247

 


 

250

 


 

267

 


 

244

 


 

265

 


 

254

 


 

245

 


 

Is there a difference in the average weights? Since there are more than 2 populations, use ANOVA

 

to see if we can prove a difference.

 

Answer the following questions:

 

a) What are the 3 populations being studied?

 

b) What are the population parameters? (Define each of them!)

 


 

c) One of the conditions for using ANOVA is that the population variances are equal. In reality, the

 

one-way ANOVA test is not too sensitive to inequality of variances if the sample sizes are equal -which they are. A rule of thumb: As long one sample variance is no more than 3-times another.

 

Is this true for our problem? Explain.

 

d)Use ANOVA and run a hypothesis test to see if it can be proven that not all the population

 

means are the same. Do this by setting up a null and alternative hypotheses and showing each

 

step by hand using a test statistic / critical value approach. Use alpha = .05.

 

e) Run the above test using a p-value / level of significance approach. Click Once for

 

instructions on using Excel to get a p-value:Example ANOVA using Excel --Include Excel file in

 

Report complete with ANOVA table.

 

f) If you were able to determine that there was a difference in the means, use Fisher's LSD to do

 

multiple pairwise tests?

 

g) What is your overall conclusion?

 


 

Part 3 Golf Wars - What's the best combination?

 

Suppose the USGA tests four different brands (A, B, C, D) of golf balls and two different clubs

 

(driver, 5-iron) in a completely randomized design. Each of the eight Brand-club combinations

 

(treatments) is randomly and independently assigned to four experimental units, each

 

experimental unit consisting of a specific position in the sequence of hits by a robotic golfer. The

 

distance response is recorded for each of the 32 hits, and are shown below:

 


 

Driver / Ball

 


 

A

 


 

B

 


 

C

 


 

D

 


 

226.4

 


 

238.3

 


 

240.5

 


 

219.8

 


 

232.6

 


 

231.7

 


 

246.9

 


 

228.7

 


 

234.0

 


 

227.7

 


 

240.3

 


 

232.9

 


 

220.7

 


 

237.2

 


 

244.7

 


 

237.6

 


 

Driver

 


 

163.8

 


 

184.4

 


 

179.0

 


 

157.8

 


 

179.4

 


 

180.6

 


 

168.0

 


 

157.8

 


 

168.6

 


 

179.5

 


 

165.2

 


 

162.1

 


 

173.4

 


 

186.2

 


 

156.5

 


 

160.3

 


 

5-Iron

 


 

Use the data to test for any significant effect due to the driver, brand of ball, and interaction.

 

a) Conduct the appropriate Two-Factor ANOVA tests (by hand) and interpret the results of your

 

analysis.

 

b) Use a test statistic / critical value approach with ?lpha = 0.10 for each test you conduct.

 

c) Run the above tests using a p-value / level of significance approach. Click Once for

 

instructions on using Excel to get a p-value:Example Two-Factor ANOVA using Excel -- Include

 

Excel file in Report complete with Two-Factor ANOVA table.

 

d) What is your overall conclusion?

 


 

 


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