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 37 of 200 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 95% confidence interval for the population proportion (to 4 decimals).

( , )

Answer 1

Solution :

Given that,

n = 200

x = 37

(a)

Point estimate = sample proportion = = x / n = 37/200=0.1850

1 -   = 1-0.1850=0.815   

(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 (((0.185*0.815) / 200)

E = 0.0538

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.185-0.0538 < p < 0.185+0.0538

0.1312< p < 0.2388

(0.1312 , 0.2388)