Question

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 #11.1.8 ("Education by age," 2013). Do the data show that educational attainment and age are independent? Test at the 5% level.

Table #11.1.8: 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	577	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	130794

Answer 1

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

for 12 degree of freedom and 0.05 level ; rejection region >21.026

applying chi square test of independence:

Expected	Ei=Σrow*Σcolumn/Σtotal	25-34	35-44	45-54	55-64	>64	Total
	not complete	11541.053	5762.052	6389.192	6330.012	7552.692	37575
	completed HS	13537.202	6758.660	7494.272	7424.855	8859.011	44074
	college 1-3 yrs	6843.852	3416.900	3788.795	3753.701	4478.751	22282
	college 4 or more yrs	8250.893	4119.388	4567.741	4525.432	5399.546	26863
	Total	40173	20057	22240	22034	26290	130794
chi square    χ2	=(Oi-Ei)2/Ei	25-34	35-44	45-54	55-64	>64	Total
	not complete	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
	college 1-3 yrs	427.833	1364.310	116.647	402.846	871.581	3183.217
	college 4 or more yrs	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

here as test statisics =22373.566 is in rejeection region ; we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that  educational attainment and age are related