Question

The FBI wants to determine the effectiveness of their 1010 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught.

Suppose a sample of 243243 suspected criminals is drawn. Of these people, 173173 were not captured. Using the data, construct the 85%85% confidence interval for the population proportion of people who are captured after appearing on the 1010 Most Wanted list. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

n = 243

x = 173

Point estimate = sample proportion = = x / n = 173 / 243 = 0.712

1 - = 1 - 0.712 = 0.288

At 85% confidence level

= 1 - 85%

=1 - 0.85 =0.15

/2 = 0.075

Z/2 = Z_{0.075 =} 1.44

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

= 1.44 (((0.712 * 0.288) / 243)

= 0.042

A 85% confidence interval for population proportion p is ,

± E  

= 0.712 ± 0.042

= ( 0.670, 0.754 )