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 246

suspected criminals is drawn. Of these people, 108 were captured. Using the data, construct the 80% 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

Given,

n = 246    ....... Sample size

x = 108    .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 108 / 246 = 0.439

Our aim is to construct 80% confidence interval.

c = 0.80

= 1- c = 1- 0.80 = 0.20

  /2 = 0.20 2 = 0.10 and 1- /2 = 0.90

Search the probability 0.90 in the Z table and see corresponding z value

  = 1.282   

Now , confidence interval for population proportion(p) is given by:

     

0.439 -1.282 *    0.439 + 1.282 *

0.439 - 0.04056   <     <   0.439 + 0.04056

0.398 <    < 0.480

is the required 90% confidence interval for the population proportion.

Required interval is (0.398 , 0.480)