Econ 2810

Intro to Statistics and Computing In Economics

Spring 2016

Problem Set 4

Out: April 7

Due: April 28

1. The data used in the table below came from a random sample.

Group 1

3.8

1.2

4.1

5.5

2.3

Group 2

5.4

2.0

4.8

3.8

Group 3

1.3

0.7

2.2

a. Complete the following ANOVA table. Please show your work.

Source

Group

df

SS

MS

F

Error

Total

b. Test the null hypothesis that µ1 = µ2 = µ3 , where µi represents the mean for group i. Use

α = 0.01.

2. Suppose the PGA wants to compare the mean distances associated with four diﬀerent brands of golf

balls when struck with a driver. From a randomized sample, data is collected from a driver hitting a

random sample of 10 balls of each brand in a random sequences. The distance is recorded for each hit,

and the results are shown in the table below.

Brand A

251.2

245.1

248

251.1

260.5

250

253.9

244.6

254.6

248.8

Brand B

263.2

262.9

265

254.5

264.3

257

262.8

264.4

260.6

255.9

Brand C

269.7

263.2

277.5

267.4

270.5

265.5

270.7

272.9

275.6

266.5

Brand D

251.6

248.6

249.4

242

246.5

251.3

261.8

249

247.1

245.9

a. Set up the null and alternative hypotheses to compare the mean distances for the four brands

b. You can use statistical software (CrunchIt) to obtain the test statistic. Use α = 0.1. At this

signiﬁcance level, can you reject the null hypothesis? Why?

[Please Turn Over]

1

2

3. The PGA is interested in knowing whether the diﬀerence in distance traveled by any two golf ball

brands depends on the club used. The PGA tests four diﬀerent brands (A,B,C,D) of golf balls and two

diﬀerent clubs (driver, ﬁve-iron) in a random experiment. The two-way table is presented below.

Club

Driver

Driver

Driver

Driver

Five-Iron

Five-Iron

Five-Iron

Five-Iron

Brand A

226.4

232.6

234

220.7

163.8

179.4

168.6

173.4

Brand B

238.3

231.7

227.7

237.2

184.4

180.6

179.5

186.2

Brand C

240.5

246.9

240.3

244.7

179

168

165.2

156.5

Brand D

219.8

228.7

232.9

237.6

157.8

161.8

162.1

160.3

a. Use statistical software (CrunchIt) to complete the following two way ANOVA table.

Source

Brand

df

SS

MS

F

P −value

Club

Brand*Club

Error

Total

b. Interpret the results of your analysis. Use α = 0.1 for each test you conduct.

4. Using CrunchIt, print out and attach the regression output using the Exercise 06 data set. The

dependent variable is the percent return on treasury bills (TBILL); the independent variable is the

rate of inﬂation.

a. Based on your regression output, is the coeﬃcient on INFLATION statistically signiﬁcant at the

1% level? Why?

b. Calculate the predicted value for TBILL when INFLATION=3.7.