Question

or 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 10,392 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

Give a brief statement of the meaning of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.1% of all confidence intervals would include the true proportion of recaptured escaped convicts.    99% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.99% of all confidence intervals would include the true proportion of recaptured escaped convicts.

(c) Is use of the normal approximation to the binomial justified in this problem? Explain.

No; np > 5 and nq < 5.Yes; np > 5 and nq > 5.    No; np < 5 and nq > 5.Yes; np < 5 and nq < 5

Answer 1

The statistic software output for this problem is:

(a) Point estimate = 0.7386

(b)

Lower limit = 0.728

Upper limit = 0.750

99% of all confidence intervals would include the true proportion of recaptured escaped convicts.

(c) Yes; np > 5 and nq > 5