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 502 judges, it was found that 295 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__ multiple choice-Give a brief interpretation of the meaning of the confidence interval you have found. A-We are 1% confident that the true proportion of judges who are introverts falls within this interval. B-We are 99% confident that the true proportion of judges who are introverts falls within this interval.C-We are 99% confident that the true proportion of judges who are introverts falls outside this interval. D-We are 1% confident that the true proportion of judges who are introverts 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. MUTIPLE CHOICE A-No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal. B-No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. C-Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial. D-Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

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 14PPS

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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 502 judges, it was found that 295 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__

multiple choice-Give a brief interpretation of the meaning of the confidence interval you have found.

A-We are 1% confident that the true proportion of judges who are introverts falls within this interval.

B-We are 99% confident that the true proportion of judges who are introverts falls within this interval.C-We are 99% confident that the true proportion of judges who are introverts falls outside this interval.

D-We are 1% confident that the true proportion of judges who are introverts 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. MUTIPLE CHOICE

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

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

C-Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

D-Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

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