Question

3. The following table presents data on the presence and absence of respiratory distress syndrome (RDS) in two groups of infants. Group 1 consisted of 42 infants whose fetal membrances ruptured 24 hours or less before delivery, while group 2 was composed of 22 infants whose membrances ruptured more than 24 hours before delivery. Test the null hypothesis that the two populations are homogeneous. Let α=.05. Incidence of respiratory distress syndrome (RDS) in two groups of infants RDS Group Yes No Total 1 27 15 42 2 7 15 22 Total 34 30 64

Answer 1

Null Hypothesis:Ho:  two populations are homogeneous

Alternate Hypothesis:Ho:  two populations are not homogeneous

degree of freedom(df) =(rows-1)*(columns-1)=		1
for 1 df and 0.05 level , critical value       χ2=		3.841
Decision rule : reject Ho if value of test statistic X2>3.841

Applying chi square test of Homogeneity:

Expected	Ei=row total*column total/grand total	yes	No	Total
	Group 1	22.31	19.69	42
	Group 2	11.69	10.31	22
	total	34	30	64
chi square    χ2	=(Oi-Ei)2/Ei	yes	No	Total
	Group 1	0.9848	1.1161	2.1008
	Group 2	1.8800	2.1307	4.0107
	total	2.8648	3.2468	6.1115
test statistic X2 =		6.1115

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that two populations are not homogeneous