In Riley county 13 out of 67 vehicles on Walsburg Road were

In Riley county, 13 out of 67 vehicles on Walsburg Road were heavy vehicles, while 32 out of 91 on North 52nd street were heavy vehicles. Find a 90% confidence interval for the difference between the percentages of heavy vehicles on the two roads.

Solution

p1=13/67 = 0.1940299

p2= 32/91 = 0.3516484

Given a=0.1, Z(0.05) = 1.645 (from standard normal table)

So 90% confidence interval is

(p1-p2) +/- Z*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

--> (0.1940299-0.3516484) +/- 1.645*sqrt(0.1940299*(1-0.1940299)/67+0.3516484*(1-0.3516484)/91)

--> (-0.272055, -0.0431819)