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 simple random sample of 220 suspected criminals is drawn. Of these people, 70 were captured. Using the data, construct the 80% confidence interval for the list. Round our answer to three decimal places.

Answer 1

Solution :

Given that,

n = 220

x = 70

Point estimate = sample proportion = = x / n = 70 / 220 = 0.318

1 - = 1 - 0.318 = 0.682

At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

Z/2 = Z_0.10 = 1.282

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

= 1.282 (((0.318 * 0.682) / 220)

= 0.040

A 80% confidence interval for population proportion p is ,

± E   

= 0.318  ± 0.040

= ( 0.278, 0.358 )