In: Math
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 3 ("Education by age," 2013). Do the data show that educational attainment and age are independent? Why or Why not? Test at the 5% level.
Education | 25-34 | 35-44 | 45-54 | 55-64 | >64 | Row Total |
Did not complete HS | 5416 | 5030 | 5777 | 7606 | 13746 | 37575 |
Completed HS | 16431 | 1855 | 9435 | 8795 | 7558 | 44074 |
College 1-3 years | 8555 | 5576 | 3124 | 2524 | 2503 | 22282 |
College 4 or more years | 9771 | 7596 | 3904 | 3109 | 2483 | 26863 |
Column Total | 40173 | 20057 | 22240 | 22034 | 26290 | 13079 |
null; hypothesis: Ho: educational attainment and age are independent.
Ha: educational attainment and age are related
degree of freedom =(row-1)*(column-1)=(4-1)*(5-1)=12
for 12 degree of freedom and 0.05 level of signfiicance rejection region >21.026
applying chi square test of independence:
Ei=Σrow*Σcolumn/Σtotal | 25-34 | 35-44 | 45-54 | 55-64 | >64 | Total |
not complete HS | 11541.053 | 5762.052 | 6389.192 | 6330.012 | 7552.692 | 37575 |
completed HS | 13537.202 | 6758.660 | 7494.272 | 7424.855 | 8859.011 | 44074 |
1-3 yrs | 6843.852 | 3416.900 | 3788.795 | 3753.701 | 4478.751 | 22282 |
>4 years | 8250.893 | 4119.388 | 4567.741 | 4525.432 | 5399.546 | 26863 |
Total | 40173 | 20057 | 22240 | 22034 | 26290 | 130794 |
=(Oi-Ei)2/Ei | 25-34 | 35-44 | 45-54 | 55-64 | >64 | Total |
not complete HS | 3250.680 | 93.005 | 58.658 | 257.211 | 5078.596 | 8738.150 |
completed HS | 618.597 | 3557.789 | 502.574 | 252.839 | 191.063 | 5122.862 |
1-3 yrs | 427.833 | 1364.310 | 116.647 | 402.846 | 871.581 | 3183.217 |
>4 years | 280.058 | 2934.133 | 96.449 | 443.334 | 1575.362 | 5329.336 |
Total | 4577.168 | 7949.237 | 774.328 | 1356.231 | 7716.602 | 22373.566 |
from above as test statistic 22373.566 is in rejection region we reject null hypothesis
we have sufficient evidence to conclude at 0.05 level that educational attainment and age are related