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 977 suspected criminals is drawn. Of these people, 400 were captured. Using the data, construct the 99% 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 = 977

x = 400

Point estimate = sample proportion = = x / n = 400 / 977 = 0.409

1 - = 1 - 0.409 = 0.591

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.409 * 0.591) / 977)

= 0.041

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.409 - 0.041 < p < 0.409 + 0.041

0.368 < p < 0.450

The 99% confidence interval for the population proportion p is : 0.368 , 0.450