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A person’s educational attainment and age group was collected by the U.S. Census Bureau in 1984...

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

Solutions

Expert Solution

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


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