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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 68 professional actors, it was found that 41 were extroverts. USE SALT (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. O We are 5% 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 within this interval. O 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 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 No, the conditions are not satisfied. This is important because it allows us to say that is approximately normal. O Yes, the conditions are 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 p is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p 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 68 professional actors, it was found that 41 were extroverts. USE SALT (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. O We are 5% 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 within this interval. O 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 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 No, the conditions are not satisfied. This is important because it allows us to say that is approximately normal. O Yes, the conditions are 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 p is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial.

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 68 professional actors, it was found that 41 were extroverts. USE SALT (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. O We are 5% 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 within this interval. O 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 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 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 p is approximately normal. O Yes, the conditions are satisfied. This is important because it allows us to say that is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that is approximately binomial.
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 68 professional actors, it was found that 41 were extroverts. USE SALT (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. O We are 5% 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 within this interval. O 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 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 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 p is approximately normal. O Yes, the conditions are satisfied. This is important because it allows us to say that is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that is approximately binomial.
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