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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 66 professional actors, it was found that 36 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) p = q= (b) Find a 95% confidence interval for p. Find the maximal margin of error. (Round your answer to two decimal places.) E = Report the bounds from the 95% 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 95% confident that the true proportion of actors who are extroverts falls within this interval. O We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. O We are 5% confident that the true proportion of actors who are extroverts falls within this interval. O We are 5% confident that the true proportion of actors who are extroverts falls above 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 Yes, the conditions are 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 binomial. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal.

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 66 professional actors, it was found that 36 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) p = q= (b) Find a 95% confidence interval for p. Find the maximal margin of error. (Round your answer to two decimal places.) E = Report the bounds from the 95% 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 95% confident that the true proportion of actors who are extroverts falls within this interval. O We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. O We are 5% confident that the true proportion of actors who are extroverts falls within this interval. O We are 5% confident that the true proportion of actors who are extroverts falls above 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 Yes, the conditions are 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 binomial. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal.

MATLAB: An Introduction with Applications
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 66 professional actors, it was found that 36 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) p â = (b) Find a 95% confidence interval for p. Find the maximal margin of error. (Round your answer to two decimal places.) E = Report the bounds from the 95% 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. We are 95% confident that the true proportion of actors who are extroverts falls within this interval. We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval. We are 5% confident that the true proportion of actors who are extroverts falls above 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. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that ô is approximately normal.
Transcribed Image Text: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 66 professional actors, it was found that 36 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) p â = (b) Find a 95% confidence interval for p. Find the maximal margin of error. (Round your answer to two decimal places.) E = Report the bounds from the 95% 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. We are 95% confident that the true proportion of actors who are extroverts falls within this interval. We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval. We are 5% confident that the true proportion of actors who are extroverts falls above 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. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that ô is approximately normal.
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