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 63 of 300 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. 

Answer 1

n = 300

x = 63

Point estimate = sample proportion = = x / n = 63/300=0.21

1 -   = 1- 0.21 =0.79

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.21*0.79) /300 )

E = 0.0461

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.21-0.0461 < p <0.21+ 0.0461

0.1639< p < 0.2561

The 95% confidence interval for the population proportion p is : 0.1639, 0.2561