Question

Are the educational aspirations of students related to family income? This question was investigated in the article “Aspirations and Expectations of High School Youth” (Int. J. of Comp. Soc. (1975): 25). The accompanying 4 X 3 table resulted from classifying 273 students according to expected level of education and family income. Does the data indicate that education aspirations and family income are not independent? Conduct hypothesis test using = .05. Income Aspired Level Low Middle High Some High School 9 11 9 High School Graduate 44 52 41 Some College 13 23 12 College Graduate 10 22 27

Answer 1

null hypothesis:Ho: education aspirations and family income are independent

alternate hypothesis:Ha: education aspirations and family income are not independent

degree of freedom(df) =(rows-1)*(columns-1)=

6

for 6 df and 0.05 level of signifcance critical region       χ2=

12.592

12.592

applying chi square test:

Expected	Ei=row total*column total/grand total	Low	middle	High	Total
	Some HS	8.0733	11.4725	9.4542	29
	HS grad	38.1392	54.1978	44.6630	137
	Some college	13.3626	18.9890	15.6484	48
	College grad	16.4249	23.3407	19.2344	59
	total	76	108	89	273
chi square    χ2	=(Oi-Ei)2/Ei	Low	middle	High	Total
	Some HS	0.1064	0.0195	0.0218	0.148
	HS grad	0.9006	0.0891	0.3004	1.290
	Some college	0.0098	0.8472	0.8506	1.708
	College grad	2.5132	0.0770	3.1352	5.725
	total	3.530	1.033	4.308	8.8709

from above as test statistic X² =8.871 is not in rejection region we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that  education aspirations and family income are not independent