) APUS CLE : MATH120 DO06

VA Homework Week 6 (AD, X

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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.

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In a random sample of 70 professional actors, it was found that 40 were extroverts.

(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.

O We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

O We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

O We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

O We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

(c) Do you think the conditions n.p > 5 and n.q > 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 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 binomial.

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

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