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 739 suspected criminals is drawn. Of these people, 236 were captured. Using the data, construct the 98% 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.

Lower endpoint?

Upper endpoint?

Answer 1

SOLUTION:

From given data,

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 739 suspected criminals is drawn. Of these people, 236 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list

n = sample = 739

= people who are captured from suspected criminals list = 236

= proportion of people who are captured from suspected criminals list = / n = 236 / 739 = 0.3193

98% = 98 / 100 = 0.98

= 1 - 0.98 =0.02

/2 = 0.02 / 2 =0.01

Z _{(1 - /2)} =  Z _{(1 - 0.01)} = Z_0.99 = 2.3263

98% CI for the population proportion of people who captured after appearing on the 10 most wanted list is,

P   (     Z_0.99   )

P   ( 0.3193    2.3263 )

P   ( 0.3193    2.3263 * 0.0171496 )

P   ( 0.3193    0.0398951 )

P   ( 0.3193-0.0398951 ,  0.3193+0.0398951 )

P   ( 0.2794049 ,  0.3591951)

P   ( 0.279 ,  0.359 )

Lower endpoint is = 0.279

Upper endpoint is = 0.359