Question

Y X1 X2 X3 21.87838 70.60643 32.53764 16.41044 93.77804 24.77081 92.403 93.99289 72.82208 22.38328 81.0025 34.85534...

Y

X1

X2

X3

21.87838

70.60643

32.53764

16.41044

93.77804

24.77081

92.403

93.99289

72.82208

22.38328

81.0025

34.85534

9.280099

34.70495

26.33653

61.68477

31.1062

61.91305

51.84463

92.25529

92.64739

17.90097

72.9859

44.74383

81.74105

36.03165

79.02588

59.32679

89.92953

21.51851

34.83117

11.82339

78.49144

48.2808

65.38289

27.14759

65.12506

73.91513

45.78317

48.29154

63.9783

42.63024

51.48476

80.61577

23.76638

81.84579

87.52321

47.18775

52.7846

14.18943

23.4629

82.91467

31.50099

90.70568

88.84991

27.21473

45.53072

54.93847

39.86673

86.99951

35.69863

27.72768

80.01956

21.69039

9.978362

58.42174

61.50215

54.04685

94.04123

72.2205

50.09629

66.52428

93.1308

51.50087

12.27189

22.93652

42.10923

68.76678

35.29041

23.17554

8.30253

9.043764

71.03076

26.70983

7.993683

7.451186

86.30393

28.6408

61.24702

31.66482

50.4105

20.05216

13.86984

75.09412

26.66686

76.40739

31.21632

94.43333

62.68383

81.74642

72.60186

13.43745

58.10215

48.42045

43.08142

70.58226

8.592578

12.14566

75.33583

72.40043

12.83587

22.06638

86.41136

30.24949

89.20978

85.65938

86.0864

38.26341

68.98163

60.13248

29.57002

22.18455

52.75237

54.18918

75.3412

32.919

24.846

11.76699

40.81475

42.46641

80.46269

9.629231

60.65081

92.06461

36.30021

28.46623

8.383099

14.21897

55.42189

25.32136

38.21238

18.43272

89.10504

35.03259

71.59474

42.34019

30.41063

72.5186

57.48445

38.01633

54.26438

91.54628

62.92822

63.21558

46.74731

35.85708

86.75781

59.27039

62.37498

62.31858

61.14228

33.42927

8.127964

91.84439

21.7629

87.34864

52.95111

87.89651

For the given data set, used in question 1; test the hypothesis that the means of variables (Y, X1 and X2) are same by using any 0.04 level of significance.    Report the Excel output as well.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: At least one means is not equal

The Excel output is:

Mean n Std. Dev
53.09780 42 28.124428 Y
46.74999 42 25.343434 X1
53.35913 42 24.482758 X2
51.06897 126 26.002528 Total
ANOVA table
Source SS    df MS F    p-value
Treatment 1,176.611051 2 588.3055256 0.87 .4222
Error 83,339.821006 123 677.5595204
Total 84,516.432058 125

The p-value is 0.4222.

Since the p-value (0.4222) is greater than the significance level (0.04), we fail to reject the null hypothesis.

Therefore, we can conclude that the means of variables (Y, X1 and X2) are the same.

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