Question

Question 24 of 31 (1 point) 9.4 Section Exercise 15 (calc) A recent random survey of 105 individuals in Michigan found that 80 drove to work alone. A similar survey of 100 commuters in New York found that 56 drivers drove alone to work. Find the 95% confidence interval for the difference in proportions. Use ê, for the proportion of Michigan drivers who drive alone to work. Round your answers to three decimal places. Use a graphing calculator. <P1-P2

Answer 1

	1st group	2nd group
x=	80	56
n =	105	100
p̂=x/n=	0.7619	0.5600
estimated diff. in proportion=p̂1-p̂2=		0.2019

Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =

0.0647

for 95 % CI value of z=		1.960	from excel:normsinv((1+0.95)/2)
margin of error E=z*std error =		0.126894
lower bound=(p̂1-p̂2)-E=		0.0750
Upper bound=(p̂1-p̂2)+E=		0.3288
from above 95% confidence interval for difference in population proportion =(0.075<p1-p2<0.329)