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.

Suppose a sample of 879 suspected criminals is drawn. Of these people, 677 were not 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

Answer 1

Solution:

Given:

Sample size = n = Number of suspected criminals selected = 879

Of these people, 677 were not captured.

thus

x = Number of people who are captured after appearing on the 10 Most Wanted list = 879 - 677 = 202

Thus the sample proportion of people who are captured after appearing on the 10 Most Wanted list is:

We have to construct the 95% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.

Formula:

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus

Thus we are 95% confident that the true population proportion of people who are captured after appearing on the 10 Most Wanted list is within the limits: