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.

Given that Sample size n =67 Favorable cases x =35 Sample proportion p^=x/n

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.

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 5E