The FBI wants to determine the effectiveness of their 10 Mos

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 716 suspected criminals is drawn. Of these people, 286 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. Also, construct the 90% 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.

Solution

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.399441341   [ANSWER, ESTIMATE OF THE PROPORTION]

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Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.018304072          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.030107519          
lower bound = p^ - z(alpha/2) * sp =   0.369333822          
upper bound = p^ + z(alpha/2) * sp =    0.42954886          
              
Thus, the confidence interval is              
              
(   0.369333822   ,   0.42954886   ) [ANSWER, CONFIDENCE INTERVAL]