Question

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 530 judges, it was found that 287 were introverts. LO USE SALT (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. O We are 99% confident that the true proportion of judges who are introverts falls outside this interval. O We are 99% confident that the true proportion of judges who are introverts falls within this interval. O We are 1% confident that the true proportion of judges who are introverts falls above this interval. O We are 1% confident that the true proportion of judges who are introverts falls within this interval. (c) Do you think the conditions np > 5 and ng > 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 binomial. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. 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 normal