Question

Question:A sociologist wishes to see whether the number of years of college a person has completed is related to their marital status. A sample of 1000 people over age 30 is selected and classified below. At ? = 0.05, can you conclude that years of college and marital status are Independent? Show all steps of the hypothesis test: Hypotheses, Alpha, Distribution, Sketch with Critical Value, Use StatCrunch to find Test Statistic and put on Sketch, Decision, Conclusion.

NO College college degree graduate degree nevermarried 103 84 61 married 97 152 136 divorced 160 87 120

Answer 1

null hypothesis: Ho: number of years of college a person has completed is not related to their marital status

alternate hypothesis:Ha: number of years of college a person has completed is related to their marital status

alpha =0.05

Distributionn is Chi square

for degree of freedom =(row-1)*(column-1)=(3-1)*(3-1) =4 and 0.05 level crtiical value =9.488

below is sketch for that:

applying chi square test of independence:

Observed	Oi	no college	college degree	graduate degree	Total
	never	103	84	61	248
	married	97	152	136	385
	divorced	160	87	120	367
	Total	360	323	317	1000
Expected	Ei=?row*?column/?total	no college	college degree	graduate degree	Total
	never	89.280	80.104	78.616	248
	married	138.600	124.355	122.045	385
	divorced	132.120	118.541	116.339	367
	Total	360	323	317	1000
chi square	=(Oi-Ei)2/Ei	no college	college degree	graduate degree	Total
	never	2.108	0.189	3.947	6.245
	married	12.486	6.146	1.596	20.227
	divorced	5.883	8.392	0.115	14.391
	Total	20.478	14.727	5.658	40.863

for above test satsitic =40.863

as test statistic falls in rejection region; we reject null hypothesis

we have sufficient evidence to conclude that   number of years of college a person has completed is related to their marital status