A sample survey is designed to estimate the proportion of sp

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A random sample of 500 registrations are selected from a Department of Motor Vehicles database, and 95 are classified as sports utility vehicles.

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)
________ to ________

Solution

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=95
Sample Size(n)=500
Sample proportion = x/n =0.19
Confidence Interval = [ 0.19 ±Z a/2 ( Sqrt ( 0.19*0.81) /500)]
= [ 0.19 - 1.96* Sqrt(0) , 0.19 + 1.96* Sqrt(0) ]
= [ 0.156,0.224]

the proportion of sports utility vehicles in California is 15.6% and 22.4%