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 34 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.)

Answer 1

Solution :

Given that,

n = 200

x = 34

Point estimate = sample proportion = = x / n = 34/200=0.17

1 - = 1-0.17=0.83

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

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

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

= 1.96 (((0.17*0.83) /200 )

E = 0.0521

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.17-0.0521 < p <0.17+ 0.0521

0.1179< p < 0.2221

The 95% confidence interval for the population proportion p is : 0.1179,0.2221