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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 38 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) 0.5588 (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) 52.9 53.1 lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. 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. 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. (C) Do you think the conditions n-p > 5 and n-q > 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 p is approximately binomial. 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 normal. Yes, the conditions are 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 68 professional actors, it was found that 38 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) 0.5588 (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) 52.9 53.1 lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. 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. 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. (C) Do you think the conditions n-p > 5 and n-q > 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 p is approximately binomial. 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 normal. Yes, the conditions are 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 68 professional actors, it was found that 38 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) 0.5588 (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) 52.9 53.1 lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. 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. 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. (C) Do you think the conditions n-p > 5 and n-q > 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 p is approximately binomial. 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 normal. Yes, the conditions are satisfied. This is important because it allows us to say that p 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 68 professional actors, it was found that 38 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) 0.5588 (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) 52.9 53.1 lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. 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. 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. (C) Do you think the conditions n-p > 5 and n-q > 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 p is approximately binomial. 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 normal. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal.
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