Question

Two samples are taken with the following numbers of successes and sample sizes
r1r1 = 24  r2r2 = 28
n1n1 = 70  n2n2 = 89

Find a 97% confidence interval, round answers to the nearest thousandth.

Answer 1

x1                =	24	x2                =	28
p̂1=x1/n1 =	24/70=0.3429	p̂2=x2/n2 =	28/89=0.3146
n1                       =	70	n2                       =	89
estimated difference in proportion   =p̂1-p̂2   =			0.0283
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0751
for 97 % CI value of z=		2.170
margin of error E=z*std error =		0.1630
lower bound=(p̂1-p̂2)-E=		-0.1347
Upper bound=(p̂1-p̂2)+E=		0.1912
from above 97% confidence interval for difference in population proportion =(-0.135,0.191)