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A person’s educational attainment and age group was collected by the U.S. Census Bureau in 1984 to see if age group and educational attainment are related.: Expert Solutions for Success

A person’s educational attainment and age group was collected by the U.S. Census Bureau in 1984 to see if age group and educational attainment are related.  The counts in thousands are in table D.  Do the data show that educational attainment and age are independent?  Test at the 5% level. Hint: Start by calculating the row and column totals. 

Table #D: Educational Attainment and Age Group 

 

Education

Age Group

Row Total

25-34

35-44

45-54

55-64

>64

Did not complete HS

5416

5030

6250

7606

13700

38002

Competed HS

17500

1900

9500

8795

7500

45195

College 1-3 years

8600

6000

3124

2524

2500

22748

College 4 or more years

9800

7500

3904

3109

2483

26796

Column Total

41316

20430

22778

22034

26183

132741

Answer

Null hypothesis: Ho: educational attainment and age are independent

Alternate hypothesis: Ha: educational attainment and age are related

Degree of freedom =(row-1)*(column-1) =(4-1)*(5-1)=12

Age group

Row total

Education

25-34

35-44

45-54

55-64

>64

 

Did not complete HS

5416

5030

6250

7606

13700

38002

Expected

11828.23

5848.84

6521.041

6308.044

7495.848

38002

 x2

3476.147

114.6379

11.2656

267.0701

5135.043

9004.163

Competed HS

17500

1900

9500

8795

7500

45195

Expected

14067.07

6955.905

7755.341

7502.027

8914.659

45195

 x2

837.7741

3674.889

392.4825

222.8435

224.4908

5352.48

College 1-3 years

8600

6000

3124

2524

2500

22748

Expected

7080.377

3501.116

3903.496

3775.996

4487.015

22748

 x2

326.1483

1783.552

155.6589

415.1204

879.9233

3560.403

College 4 or more years

9800

7500

3904

3109

2483

26796

Expected

8340.328

4124.139

4598.122

4447.933

5285.478

26796

 x2

255.4625

2763.35

104.783

403.0505

1485.936

5012.583

Column Total

41316

20430

22778

22034

26183

132741

Expected

41316

20430

22778

22034

26183

132741

 x2

4895.532

8336.429

664.19

1308.084

7725.393

22929.63

 

The chi-square for this data is thus 22929.63 and the p-value from the chi-square table is 0.0000. Since the p-value is less than alpha value; that is 0.0000 < 0.05, there is sufficient evidence to reject the null hypothesis and conclude that the educational attainment and age are related.

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