Question

Assume that you plan to use a significance level of \alphaα = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate p-bar. Round your answer to the nearest thousandth. n1 = 236 n2 = 307 x1 = 77 x2 = 66

Answer 1

null Hypothesis:    Ho:    p1-p2		=	0.00
alternate Hypothesis: Ha:   p1-p2		≠	0.00

for 0.05 level with two tailed test , critical value of z=			1.960
Decision rule :                   reject Ho if absolute value of test statistic |z|>1.96

	Pop 1		Pop 2
x1                =	77	x2                =	66
p̂1=x1/n1 =	0.3263	p̂2=x2/n2 =	0.2150
n1                       =	236	n2                       =	307
estimated prop. diff =p̂1-p̂2    =		0.1113
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.2634
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0381
test stat z=(p̂1-p̂2)/Se =		2.92

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that population proportions are not equal