Question

An insurance company checks police records of 560 accidents selected at random and found that teenagers were at the wheel in 18% of them. Construct a 95% confidence interval for the true percentage of auto accidents that involve teenage drivers. Interpret your results.

Answer 1

Solution :

Given that,

n = 560

Point estimate = sample proportion = = 0.18

1 -   = 1- 0.18 =0.82

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 (((0.18*0.82) /560 )

E = 0.0318

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.18-0.0318 < p <0.18+ 0.0318

0.1482< p < 0.2118

The 95% confidence interval for the population proportion p is : 0.1482,0.2118