Question

According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the CNBC report, showed 16 of 180 vehicles were not covered by insurance.

a. What is the point estimate of the proportion of vehicles not covered by insurance (to 4 decimals)?

( )

b. Develop a  confidence interval for the population proportion (to 4 decimals).

( , )

Answer 1

a) n= 180

x = 16

p = 16/180 = 0.0889

b) Taking 95% interval:

Standard error of the mean = SEM = √x(N-x)/N³ = 0.021

α = (1-CL)/2 = 0.025

Standard normal deviate for α = Z_α = 1.960

Proportion of positive results = P = x/N = 0.089

Lower bound = P - (Z_α*SEM) = 0.047

Upper bound = P + (Z_α*SEM) = 0.130