For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 540 judges, it was found that 287 were introverts. USE SALT (a) Let p represent the proportion of all judges who are introverts. 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 two decimal places.) lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. O We are 99% confident that the true proportion of judges who are introverts falls outside this interval. O We are 99% confident that the true proportion of judges who are introverts falls within this interval. O We are 1% confident that the true proportion of judges who are introverts falls above this interval. O We are 1% confident that the true proportion of judges who are introverts falls within this interval. (c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal. O Yes, the conditions are satisfied. This is important because it allows us to say that is approximately binomial.
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 540 judges, it was found that 287 were introverts. USE SALT (a) Let p represent the proportion of all judges who are introverts. 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 two decimal places.) lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. O We are 99% confident that the true proportion of judges who are introverts falls outside this interval. O We are 99% confident that the true proportion of judges who are introverts falls within this interval. O We are 1% confident that the true proportion of judges who are introverts falls above this interval. O We are 1% confident that the true proportion of judges who are introverts falls within this interval. (c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal. O Yes, the conditions are satisfied. This is important because it allows us to say that is approximately binomial.
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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For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
In a random sample of 540 judges, it was found that 287 were introverts.
![### Statistical Analysis of Proportion of Introverted Judges
#### Given Data:
In a random sample of 540 judges, it was found that 287 were introverts.
---
#### Tasks:
**(a)** Let \( p \) represent the proportion of all judges who are introverts. Find a point estimate for \( p \). (Round your answer to four decimal places.)
\[ \text{Point Estimate:} \ \_\_\_\_\_ \]
**(b)** Find a 99% confidence interval for \( p \). (Round your answers to two decimal places.)
**Confidence Interval for \( p \):**
- Lower limit: \_\_\_\_\_\_\_
- Upper limit: \_\_\_\_\_\_\_
---
#### Interpretation of the Confidence Interval:
Give a brief interpretation of the meaning of the confidence interval you have found.
- [ ] We are 99% confident that the true proportion of judges who are introverts falls outside this interval.
- [ ] We are 99% confident that the true proportion of judges who are introverts falls within this interval.
- [ ] We are 1% confident that the true proportion of judges who are introverts falls above this interval.
- [ ] We are 1% confident that the true proportion of judges who are introverts falls within this interval.
---
**(c)** Do you think the conditions \( np > 5 \) and \( n(1-p) > 5 \) are satisfied in this problem? Explain why this would be an important consideration.
- [ ] No, the conditions are not satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately binomial.
- [ ] Yes, the conditions are satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately normal.
- [ ] No, the conditions are not satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately normal.
- [ ] Yes, the conditions are satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately binomial.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe76f06b-a6e5-4577-ae94-392ea27c231a%2Fa57aaaf1-70f5-4770-bcfb-1ea411cf9690%2Fawo3ncq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Proportion of Introverted Judges
#### Given Data:
In a random sample of 540 judges, it was found that 287 were introverts.
---
#### Tasks:
**(a)** Let \( p \) represent the proportion of all judges who are introverts. Find a point estimate for \( p \). (Round your answer to four decimal places.)
\[ \text{Point Estimate:} \ \_\_\_\_\_ \]
**(b)** Find a 99% confidence interval for \( p \). (Round your answers to two decimal places.)
**Confidence Interval for \( p \):**
- Lower limit: \_\_\_\_\_\_\_
- Upper limit: \_\_\_\_\_\_\_
---
#### Interpretation of the Confidence Interval:
Give a brief interpretation of the meaning of the confidence interval you have found.
- [ ] We are 99% confident that the true proportion of judges who are introverts falls outside this interval.
- [ ] We are 99% confident that the true proportion of judges who are introverts falls within this interval.
- [ ] We are 1% confident that the true proportion of judges who are introverts falls above this interval.
- [ ] We are 1% confident that the true proportion of judges who are introverts falls within this interval.
---
**(c)** Do you think the conditions \( np > 5 \) and \( n(1-p) > 5 \) are satisfied in this problem? Explain why this would be an important consideration.
- [ ] No, the conditions are not satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately binomial.
- [ ] Yes, the conditions are satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately normal.
- [ ] No, the conditions are not satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately normal.
- [ ] Yes, the conditions are satisfied. This is important because it allows us to say that \( \hat{p} \) is approximately binomial.
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