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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.

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
Education	25-34	35-44	45-54	55-64	>64	Row Total
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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