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# Chi-square Distribution Essay Example

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## Chi-square Distribution

Chi-square Distribution. The answers to possible questions from the variables could ‘yes, there is a relationship between sales and use of software’ or ‘no’ (Bowerman, OConnell, Orris & Murphree, 2010).Considering the distribution of the sales force of WidgeCorp, it is convenient to assume that in each region, there are 500 sales persons which give the total of 500. Since we are told that only half of this number was given the software during the test period, we hypothesize that suppose this number is equally divided for the Southeast and the West region, then all of the agents in these two regions were given the software leading to the chi-square analysis below.From the calculations, we obtain a chi-square of 2.

62 with a degree of freedom for the data set 1 (obtained from rows and columns). From the chi distribution table in appendix 1 with section provided below, we obtain a chi-square probability of 3.81 which is greater than the calculated x2 and we, therefore, reject the null hypothesis in this regard. The calculations prove an adequate dependence on sales on the use of the software.Ha: sales in NE=sales in SE= Sales in Central =- sales in West. Consequently, the null hypothesis, in this case, will be that the alternative hypothesis is not true where the sales volume in the three regions will not be the same but very (Bartholomew, Steele, Moustaki, & Galbraith, 2002). We develop the contingency table below and test as in the subsequent table.Therefore, considering a probability level (alpha) of 0.05 and checking on the chi distribution table given as appendix 1 against the degree of freedom obtained we find a probability of 7.815 which is far less than our computed chi-squared value of 37. This, therefore, confirms the positive hypothesis of a relationship between the use of software and volume of sales and so we reject the null hypothesis.Chi-square test rejects the null hypothesis that all the sales agents of company W must sale same volume of the software and so we realize a variation in sales for those who used the software and those who did not use the software. We find from the analysis, that those who did not use the software sold more but cannot hastily conclude based on the sales volume but through the chi-squared test. Chi-square Distribution.

References

Bartholomew, D.J., Steele, F., Moustaki, I., & Galbraith, J. I. (2002). The analysis and interpretation of multivariate data for social scientist. Chapman & HaLL/CRC.

Bowerman, B.L., O'Connell, R. T., Orris, J. B. & Murphree, E. S. (2010) Essential of Business Statistics (3rd E.d.) McGraw Hill Irwin Boston, New York

Career Education Corporation (2007) Statistical test conclusions

Chi-square table of critical values. (n.d.). Statistics help. Retrieved November 2, 2012, from http://www.statisticsmentor.com/tables/table_chi.htm

Appendix I: Chi alpha distribution table

α

0.995

0.99

0.975

0.95

0.9

0.1

0.05

0.025

0.01

0.005

df=1

---

---

0.001

0.004

0.016

2.706

3.841

5.024

6.635

7.879

2

0.01

0.02

0.051

0.103

0.211

4.605

5.991

7.378

9.21

10.597

3

0.072

0.115

0.216

0.352

0.584

6.251

7.815

9.348

11.345

12.838

4

0.207

0.297

0.484

0.711

1.064

7.779

9.488

11.143

13.277

14.86

5

0.412

0.554

0.831

1.145

1.61

9.236

11.07

12.833

15.086

16.75

6

0.676

0.872

1.237

1.635

2.204

10.645

12.592

14.449

16.812

18.548

7

0.989

1.239

1.69

2.167

2.833

12.017

14.067

16.013

18.475

20.278

8

1.344

1.646

2.18

2.733

3.49

13.362

15.507

17.535

20.09

21.955

9

1.735

2.088

2.7

3.325

4.168

14.684

16.919

19.023

21.666

23.589

10

2.156

2.558

3.247

3.94

4.865

15.987

18.307

20.483

23.209

25.188

11

2.603

3.053

3.816

4.575

5.578

17.275

19.675

21.92

24.725

26.757

12

3.074

3.571

4.404

5.226

6.304

18.549

21.026

23.337

26.217

28.3

13

3.565

4.107

5.009

5.892

7.042

19.812

22.362

24.736

27.688

29.819

14

4.075

4.66

5.629

6.571

7.79

21.064

23.685

26.119

29.141

31.319

15

4.601

5.229

6.262

7.261

8.547

22.307

24.996

27.488

30.578

32.801

16

5.142

5.812

6.908

7.962

9.312

23.542

26.296

28.845

32

34.267

17

5.697

6.408

7.564

8.672

10.085

24.769

27.587

30.191

33.409

35.718

18

6.265

7.015

8.231

9.39

10.865

25.989

28.869

31.526

34.805

37.156

19

6.844

7.633

8.907

10.117

11.651

27.204

30.144

32.852

36.191

38.582

20

7.434

8.26

9.591

10.851

12.443

28.412

31.41

34.17

37.566

39.997

21

8.034

8.897

10.283

11.591

13.24

29.615

32.671

35.479

38.932

41.401

22

8.643

9.542

10.982

12.338

14.041

30.813

33.924

36.781

40.289

42.796

23

9.26

10.196

11.689

13.091

14.848

32.007

35.172

38.076

41.638

44.181

24

9.886

10.856

12.401

13.848

15.659

33.196

36.415

39.364

42.98

45.559

25

10.52

11.524

13.12

14.611

16.473

34.382

37.652

40.646

44.314

46.928

26

11.16

12.198

13.844

15.379

17.292

35.563

38.885

41.923

45.642

48.29

27

11.808

12.879

14.573

16.151

18.114

36.741

40.113

43.195

46.963

49.645

28

12.461

13.565

15.308

16.928

18.939

37.916

41.337

44.461

48.278

50.993

29

13.121

14.256

16.047

17.708

19.768

39.087

42.557

45.722

49.588

52.336

30

13.787

14.953

16.791

18.493

20.599

40.256

43.773

46.979

50.892

53.672

40

20.707

22.164

24.433

26.509

29.051

51.805

55.758

59.342

63.691

66.766

50

27.991

29.707

32.357

34.764

37.689

63.167

67.505

71.42

76.154

79.49

60

35.534

37.485

40.482

43.188

46.459

74.397

79.082

83.298

88.379

91.952

70

43.275

45.442

48.758

51.739

55.329

85.527

90.531

95.023

100.425

104.215

80

51.172

53.54

57.153

60.391

64.278

96.578

101.879

106.629

112.329

116.321

90

59.196

61.754

65.647

69.126

73.291

107.565

113.145

118.136

124.116

128.299

100

67.328

70.065

74.222

77.929

82.358

118.498

124.342

129.561

135.807

140.169

Source: http://www.statisticsmentor.com/tables/table_chi.htm

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