Question

The following data represent the level of health and the level of education for a random sample of 1815 residents.	Education	Excellent	Good	Fair	Poor
	Not a H.S. graduate	105	148	105	116
	H.S. graduate	118	129	110	119
	Some college	116	146	117	124
	Bachelor Degree or higher	68	142	59	93

Make the proper conclusion. Choose the correct answer below.

A. Fail to reject H0. There is sufficient evidence that level of education and health are associated.

B. Reject H0. There is not sufficient evidence that level of education and health are associated.

C. Fail to reject H0. There is not sufficient evidence that level of education and health are associated.

D. Reject H0. There is sufficient evidence that level of education and health are associated.

Answer 1

Claim: There is an association between level of education and health.

The null and alternative hypothesis is

H0: There is no association between level of education and health.

H1: There is an association between level of education and health.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

	Excellent	Good	Fair	Poor	Total
	105	148	105	116	474
	118	129	110	119	476
	116	146	117	124	503
	68	142	59	93	362
Total	407	565	391	452	1815

O	E	(O-E)	(O-E)^2	(O-E)^2/E
105	106.2909	-1.29091	1.666446	0.015678
148	147.5537	0.446281	0.199167	0.00135
105	102.1124	2.887603	8.338253	0.081658
116	118.043	-2.04298	4.173748	0.035358
118	106.7394	11.26061	126.8012	1.187952
129	148.1763	-19.1763	367.7308	2.481711
110	102.5433	7.456749	55.60311	0.542241
119	118.541	0.458953	0.210638	0.001777
116	112.7939	3.206061	10.27882	0.091129
146	156.5813	-10.5813	111.9632	0.715049
117	108.3598	8.64022	74.65341	0.68894
124	125.265	-1.26501	1.60026	0.012775
68	81.17576	-13.1758	173.6006	2.138577
142	112.6887	29.31129	859.152	7.624118
59	77.98457	-18.9846	360.414	4.621607
93	90.15096	2.849036	8.117005	0.090038
			Total	20.330

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 4 - 1) * (4 - 1) = 3 * 3 = 9

Level of significance = 0.05

Critical value = 16.919

( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

D. Reject H0. There is sufficient evidence that level of education and health are associated.