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 1 of 2: Suppose a sample of 465 suspected criminals is drawn. Of these people, 111 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Step 2 of 2: Suppose a sample of 465 suspected criminals is drawn. Of these people, 111 were captured. Using the data, construct the 85% 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=465, X=111
p^=X/n
=111/465
=0.2387
= 0.239 .... upto 3 decimal place.
Point estimate of p=p^ = 0.239
(1–α)%=85%
α=0.15
α/2=0.075
Zα/2=1.44 ....... from standard normal table.
Margin of error=E=Zα/2 ×√{[p^(1-p^)]/n}
=1.44 ×√{[0.239(1-0.239)]/465}
=0.0285
Margin of error=E=0.0285
85% Confidence Interval for population proportion of the people who are captured after appearing on the 10 most wanted list is given as,
p^ ± Margin of error=(0.239-0.0285,0.239+0.0285)
=(0.2105,0.2675)
=(0.210,0.267) ....upto 3 decimal place.
Lower limit =0.210
Upper limit=0.267