Question

Out of a sample of n=10351 prisoners who escaped US prisons, x=7867 were recaptured. Based upon this sample, we wish to estimate p, the true probability of a prison escapee being recaptured. Assume this is a random sample from the population of all prisoners who escape from US prisons and let unknown p be the true percentage of such prisoners who are recaptured. Let p? be the sample proportion of escaped prisoners who are recaptured. Answer the following using R code.

c) Calculate p?.

h) Assuming the same p? value, what sample size would have made the 97% confidence interval for p have a length of .01 or less?

Answer 1

c)

$\hat{p}$ = 7867/10351 = 0.76

h)

ME2

(0.76-024) 115525747246. 0.01

n~2575