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 23 of 236 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 99% confidence interval for the population proportion (to 4 decimals).

Answer 1

Given that according to the CNBC report out of n= 236 vehicles X = 23 vehicles were not covered by insurance.

a) The point estimate of the proportion of vehicles not covered by insurance is the sample proportion which is calculated as:

b) The confidence interval is calculated as:

Where Zc is the critical score at 99% confidence level which is computed using the excel formula for normal distribution which is =NORM.D.INV(0.99), thus the Zc is computed as 2.576.

Now the confidence interval is calculated as:

CI = { 0.0478, 0.1472 }