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In a random sample of 67 professional actors, it was found that 35 were extroverts. LAUSE SALT (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.) (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit Give 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 outside this interval. O We are 5% confident that the true proportion of actors who are extroverts falls above this interval. O We are 95% confident that the true proportion of actors who are extroverts 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 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 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.

In a random sample of 67 professional actors, it was found that 35 were extroverts. LAUSE SALT (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.) (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit Give 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 outside this interval. O We are 5% confident that the true proportion of actors who are extroverts falls above this interval. O We are 95% confident that the true proportion of actors who are extroverts 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 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 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.

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 67 professional actors, it was found that 35 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.) \[ \boxed{} \] ### (b) Find a 95% confidence interval for \( p \). (Round your answers to two decimal places.) lower limit \[ \boxed{} \] upper limit \[ \boxed{} \] ### 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 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. - ○ We are 95% confident that the true proportion of actors who are extroverts 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. - ○ 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 binomial. - ○ 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.
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 67 professional actors, it was found that 35 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.) \[ \boxed{} \] ### (b) Find a 95% confidence interval for \( p \). (Round your answers to two decimal places.) lower limit \[ \boxed{} \] upper limit \[ \boxed{} \] ### 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 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. - ○ We are 95% confident that the true proportion of actors who are extroverts 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. - ○ 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 binomial. - ○ 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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