Question

According to statistics reported on news source, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the news report, showed 48 of 200 vehicles were not covered by insurance.

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

(b) Develop a 95% confidence interval for the population proportion. (Round your answer to four decimal places.) ___to___

Answer 1

Solution :

Given that,

n = 200

x = 48

a)

Point estimate = sample proportion = = x / n = 48/200=0.24

1 -   = 1- 0.24 =0.76

b)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.24*0.76) /200 )

E = 0.0592

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.24-0.0592 < p < 0.24+0.0592

0.1808< p < 0.2992

_0.1808_to__0.2992_