Question

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2 : Suppose a sample of 539 suspected criminals is drawn. Of these people, 204 were captured. Using the data, construct the 95 % confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

n = 539

x = 204

= x / n =204 /539 =0.378

1 - = 1 - 0. 378= 0.622

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

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

= 1.96 * (((0.378* 0.622) / 539) = 0.041

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.378 - 0.041 < p < 0.378+ 0.041

0.337 < p < 0.419

The 95% confidence interval for the population proportion p is : ( 0.337 , 0.419)