For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to ro

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For This Problem Carry At Least Four Digits After The Decimal In Your Calculations Answers May Vary Slightly Due To Ro 1 (211.37 KiB) Viewed 7 times

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 61 professional actors, it was found that 45 were extroverts. USE 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 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 outside this interval. 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. 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 is approximately binomial. 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 is approximately normal. No, the conditions are not satisfied. This is important because t allows us to say that p is approximately normal. -/4.42 Points] DETAILS 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 538 judges, it was found that 277 were introverts. USE SALT BBUNDERSTAT12 7.3.012.MI.S. (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% 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 99% confident that the true proportion of judges who are introverts falls within this interval. We are 1% confident that the true proportion of judges who are introverts falls above this interval. We are 1% confident that the true proportion of judges who are introverts falls within this interval. We are 99% confident that the true proportion of judges who are introverts falls outside 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 is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that is approximately normal. No, the conditions are not 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 p is approximately normal.