For this problem, carry at least four digits after the decimal in your calculati

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 518 judges, it was found that 278 were introverts. a) Lat p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.) 0.5367 (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 1% confident that the true proportion of judges who are introverts falls within this interval. O we are 99% confident that the true proportion of judges who are introverts falls outside this interval. O we are 1% confident that the true proportion of judges who are introverts falls above this interval. e, we are 99% 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 bocause 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 normal. O No, the conditions are not satisfied. This is important because it allowws us to say that is approximately binomial O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal. Need Help? Reod

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

99% confidence interval results:

Hence,

a) Point estimate = 0.5367

b) 99% confidence interval:

Lower limit = 0.48

Upper limit = 0.59

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 278 518 0.53667954 0.021909546 0.48024429 0.59311479

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