Answered: For this problem, carry at least four…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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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 514 judges, it was found that 287 were introverts.

(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 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. We are 1% confident that the true proportion of judges who are introverts falls above this interval.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 nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

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