Question

Compute the test statistic used to test the null hypothesis that p1 = p2. In a vote on the Clean Water bill, 43% of the 205 Democrats and 44% of 230 Republicans voted for the bill.

please explain using Excel

Answer 1

	Democrats		Republicans
p̂1=x1/n1 =	0.4300	p̂2=x2/n2 =	0.4400
n1                       =	205	n2                       =	230
estimated prop. diff =p̂1-p̂2    =0.43-0.44=		-0.0100
pooled prop p̂ =(x1+x2)/(n1+n2)=(0.43*205+0.44*230)/(205+230)=		0.4353
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =sqrt(0.4353*(1-0.4353)*(1/205+1/230)=		0.0476
test stat z=(p̂1-p̂2)/Se =-0.01/0.0476 =		-0.21