13 value 142 points A sample of 41 homes in a subdivision re

13.

value:
1.42 points

A sample of 41 homes in a subdivision revealed that 29 were ranch style (as opposed to colonial, tri-level, or Cape Cod).

Construct a 95 percent confidence interval for the true proportion of ranch style homes. (Round your answers to 4 decimal places.)

Solution

(a) p=29/41=0.7073171

Given a=0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n ) = 0.7073171-1.96*sqrt(0.7073171*(1-0.7073171)/41) =0.5680

So the upper bound is

p + Z*sqrt(p*(1-p)/n ) = 0.7073171+1.96*sqrt(0.7073171*(1-0.7073171)/41) =0.8466

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(b)Yes