Question

The FBI wants to determine the effectiveness of their 1010 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. In an earlier study, the population proportion was estimated to be 0.350.35.

How large a sample would be required in order to estimate the fraction of people who are captured after appearing on the 1010 Most Wanted list at the 80%80% confidence level with an error of at most 0.040.04? Round your answer up to the next integer.

Answer 1

Given that 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. In an earlier study, the population proportion was estimated to be p = 0.35.

Now a sample that would be required in order to estimate the fraction of people who are captured after appearing on the 10 Most Wanted list at the 80% confidence level with an error of at most E = 0.04 is calculated as:

Where Zc at 80% confidence level is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.90), thus the Zc is computed as 1.282. Now the minimum sample is calculated as:

Thus a minimum of N = 234 sample is required.