Question

2. Blood pressure is independent of the blood group. We want to know, if the distributions attending to the blood group, in three referred samples attending to the type of blood pressure, they are distributed in the same way. To this end, a sample of 1500 subjects was collected and their blood group was determined and blood pressure was taken, classifying it as low, normal, and high. Obtaining the following results:

Blood pressure	Blood Grpoup
	A	B	AB	O	Total
Low	28	9	7	31	75
Normal	543	211	90	476	1320
High	44	22	8	31	105
Total	615	242	105	538	1500

Use alfa at 0.05

Answer 1

null hypothesis: Ho : distributions attending to the blood group, in three referred samples attending to the type of blood pressure, are distributed in the same way

alternate hypothesis: distributions attending to the blood group, in three referred samples attending to the type of blood pressure, are not distributed in the same way

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

6

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

12.592

Applying chi square test of independence:

Expected	Ei=Σrow*Σcolumn/Σtotal	A	B	AB	O	Total
	low	30.7500	12.1000	5.2500	26.9000	75
	normal	541.2000	212.9600	92.4000	473.4400	1320
	high	43.0500	16.9400	7.3500	37.6600	105
	Total	615	242	105	538	1500
chi square    χ2	=(Oi-Ei)2/Ei	A	B	AB	O	Total
	low	0.2459	0.7942	0.5833	0.6249	2.248
	normal	0.0060	0.0180	0.0623	0.0138	0.100
	high	0.0210	1.5114	0.0575	1.1778	2.768
	Total	0.273	2.324	0.703	1.817	5.1163

test statistic =5.116

Decision: as test statitic is not in rejection region we fail to reject null hypothesis

Conclusion:we do not have sufficient evidence to conclude that distributions attending to the blood group, in three referred samples attending to the type of blood pressure, are not distributed in the same way