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 |
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 |
||
|
|
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 |
||
|
|
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 |
||
|
|
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 |
||
|
|
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 |
||
|
|
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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