Question

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 10,035 convicts who escaped from certain prisons, only 7676 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.)

lower limit
upper limit

Answer 1

a)

Number of Items of Interest,   x =   7676
Sample Size,   n =    10035

point estimate for p=p̂ = x/n =    0.7649

b)

Level of Significance,   α =    0.01

      
Sample Proportion ,    p̂ = 0.7649
z -value =   "Zα/2 = 2.5758 [excel function =normsinv(0.01/2)

Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0042
      
margin of error ,    E = Z*SE =    0.0109
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.754
Interval Upper Limit , =    p̂ + E =   0.776