## [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.

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.

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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