Question

Efficacy of a new drug, referred to as Drug 2 is tested over the already existing drug,referred to as Drug 1, for a particular disease. The data on the number of people usingDrug 1 and Drug 2 vs. people who are cured or not cured are given in Table 1. Test H0 that there is no difference between Drug 1 and Drug 2 in curing people, at 5% level of significance. Use

P(X12 > 3.84) = 0.05

table 1:

	cured	not cured	total
drug 1	37	13	50
drug 2	88	21	109
total	125	34	159

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	cured	not cured	Total
	Drug 1	39.310	10.692	50.00
	Drug 2	85.692	23.308	109.00
	total	125.00	34.00	159.00
chi square    χ2	=(Oi-Ei)2/Ei	cured	not cured	Total
	Drug 1	0.136	0.498	0.6340
	Drug 2	0.062	0.229	0.2907
	total	0.1979	0.7269	0.925
test statistic X2 =		0.925

since test statistic X² =0.925 <3.84 :

we fail to reject null hypothesis

we do not have sufficient evidence to reject the hypothesis that there is no difference between Drug 1 and Drug 2 in curing people,