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 10,205 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.) lower limit upper limit Give a brief statement of the meaning of the confidence interval. O We are 99% confident that the true proportion of recaptured escaped convicts falls outside this interval. O We are 1% confident that the true proportion of recaptured escaped convicts falls within this interval. O We are 99% confident that the true proportion of recaptured escaped convicts falls within this interval. O We are 1% confident that the true proportion of recaptured escaped convicts falls above this interval. (c) Is use of the normal approximation to the binomial justified in this problem? Explain. O No; np > 5 and ng < 5. O Yes; np < 5 and ng < 5. O Yes; np > 5 and ng > 5. O No; np < 5 and ng > 5.
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 10,205 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.) lower limit upper limit Give a brief statement of the meaning of the confidence interval. O We are 99% confident that the true proportion of recaptured escaped convicts falls outside this interval. O We are 1% confident that the true proportion of recaptured escaped convicts falls within this interval. O We are 99% confident that the true proportion of recaptured escaped convicts falls within this interval. O We are 1% confident that the true proportion of recaptured escaped convicts falls above this interval. (c) Is use of the normal approximation to the binomial justified in this problem? Explain. O No; np > 5 and ng < 5. O Yes; np < 5 and ng < 5. O Yes; np > 5 and ng > 5. O No; np < 5 and ng > 5.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Transcribed Image Text:**Instructions for Statistical Problem**
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
**Case Study:**
Out of 10,205 convicts who escaped from certain prisons, only 7,958 were recaptured.
**Tasks:**
(a) **Point Estimate:**
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.)
*Input Box for Point Estimate*
(b) **Confidence Interval:**
Find a 99% confidence interval for \( p \). (Round your answers to three decimal places.)
*Input Box for Lower Limit*
*Input Box for Upper Limit*
**Confidence Interval Statement:**
Give a brief statement of the meaning of the confidence interval.
- ○ We are 99% confident that the true proportion of recaptured escaped convicts falls outside this interval.
- ○ We are 1% confident that the true proportion of recaptured escaped convicts falls within this interval.
- ○ We are 99% confident that the true proportion of recaptured escaped convicts falls within this interval.
- ○ We are 1% confident that the true proportion of recaptured escaped convicts falls above this interval.
(c) **Normal Approximation:**
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 \( nq > 5 \).
Expert Solution
Step 1
Given data:
n = 10206
x = 7958
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Solved in 3 steps with 2 images
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