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 10,630 convicts who escaped from certain prisons, only 7629 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. 99% 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 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. Yes; np > 5 and nq > 5.

Answer 1

The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

99% confidence interval results:

Proportion	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
p	7629	10630	0.71768579	0.0043658309	0.70644016	0.72893143

Hence,

a) Point estimate = 0.718

b) 99% confidence interval: (0.706, 0.729)

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

c) Yes; np > 5 and nq > 5