For this problem carry at least four digits after the decima

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Case studies showed that out of 10,783 convicts who escaped from certain prisons, only 7535 were recaptured.

(a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

Solution

A)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.698785125   [ANSWER]

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B)      
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.004418148          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.011380394          
lower bound = p^ - z(alpha/2) * sp =   0.68740473          
upper bound = p^ + z(alpha/2) * sp =    0.710165519          
              
Thus, the confidence interval is              
              
(   0.68740473   ,   0.710165519   ) [ANSWER]