Question

Use a 0.03 significance level to test the claim that the proportion of men who plan to vote in the next election is the same as the proportion of women who plan to vote (homogeneous). Men and Women were randomly selected and asked whether they planned to vote in the next election. The results are shown below. Show all work please

                    / Men / Women
Plan to Vote        / 93 /  158
Do Not Plan to Vote / 116 /  91

Answer 1

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

for 0.03 level with two tailed test , critical value of z=			2.170
Decision rule : reject Ho if absolute value of test statistic |z|>2.17

	men	women
x=	93	158
p̂=x/n=	93/209=0.4450	158/249=0.6345
n =	209	249
estimated prop. diff =p̂1-p̂2    =0.4450-0.6345=		-0.1896
pooled prop p̂ =(x1+x2)/(n1+n2)=(93+158)/(209+249)=		0.5480
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0467
test stat z=(p̂1-p̂2)/Se =(-0.1896-0)/0.0467=		-4.06

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that the proportion of men who plan to vote in the next election is not the same as the proportion of women who plan to vote