Please Use R

1. (10) A soft drink manufacturer uses five agents to handle premium distributions for its various products. The marketing director desired to study the timeliness with which the premiums are distributed. Twenty transactions for each agent were selected at random, and the time lapse (in days) for handling each transaction was determined. The results are in premium.txt.

a)Obtain the fitted values.

b) Obtain the residues. Do they sum to zero as in the regression model?

c) Obtain the analysis of variance table.

d) Test whether or not the mean time lapse differs for the five agents; useState the alternatives, decision rule, and conclusion.

e)Test assumption for the test.

24.011

24.012

29.013

20.014

21.015

25.016

28.017

27.018

23.019

21.0110

24.0111

26.0112

23.0113

24.0114

28.0115

23.0116

23.0117

27.0118

26.0119

25.0120

18.021

20.022

20.023

24.024

22.025

29.026

23.027

24.028

28.029

19.0210

24.0211

25.0212

21.0213

20.0214

24.0215

22.0216

19.0217

26.0218

22.0219

21.0220

10.031

11.032

8.033

12.034

12.035

10.036

14.037

9.038

8.039

11.0310

16.0311

12.0312

18.0313

14.0314

13.0315

11.0316

14.0317

9.0318

11.0319

12.0320

15.041

13.042

18.043

16.044

12.045

19.046

10.047

18.048

11.049

17.0410

15.0411

12.0412

13.0413

13.0414

14.0415

17.0416

16.0417

17.0418

14.0419

16.0420

33.051

22.052

28.053

35.054

29.055

28.056

30.057

31.058

29.059

28.0510

33.0511

30.0512

32.0513

33.0514

29.0515

35.0516

32.0517

26.0518

30.0519

29.0520

2. (6) Refer toproblem 1, suppose that 25 percent of all premium distribution are handled by agent1, 20 percent by agent 2, 20 percent by agent 3, 20 percent by agent 4, and 15 percent by agent 5.

a) Obtain a point estimate of the grand mean. when the ANOVA model is expressed in the factor effects with the weighs being the proportions of premium distribution handled by each agent.

b) Test whether or not the mean lapse differs for the five agents; useState the alternatives, decision rule, and conclusion.

3. (8) Refer to problem 1,

a) Construct a 90% confidence interval for the mean time lapse for agent 1.

b) Obtain a 90% confidence interval for. Interpret your interval estimate.

c) The marketing director wishes to compare the mean time lapses for agents 1, 3, and 5. Obtain confidence interval for all pairwise comparisons among these three treatment means; use the Bonferroni procedure with a 90% family level.

4. (6) Refer to problem 1, suppose primary interest is in estimating the following comparisons:

a) Obtain a 90% confidence interval for individual comparison.

b) Obtain a 90% simultaneous confidence interval for the two comparisons.