For this problem, carry at least four digits after the decimal in your calculati
ID: 3063637 • Letter: F
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 10,477 convicts who escaped from certain prisons, only 7958 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.)
(c) 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.
(d) 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.
No; np > 5 and nq < 5.
Explanation / Answer
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:
Hence,
a) Point estimate = 0.7596
b) 99% confidence interval: (0.7488, 0.7703)
c) 99% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.
d) Yes; np > 5 and nq > 5
Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 7958 10477 0.75956858 0.0041750399 0.74881439 0.77032277Related Questions
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