For this problem, carry at least four digits after the decimalin your calculations. Answers may vary slightly due torounding.
In a random sample of 67 professional actors, it was found that 44were extroverts.
(a) Let p represent the proportion of all actors whoare extroverts. Find a point estimate for p. (Round youranswer to four decimal places.)
(b) Find a 95% confidence interval for p. (Round youranswers to two decimal places.)
| lower limit    | |
| upper limit    | |
Give a brief interpretation of the meaning of the confidenceinterval you have found.
We are 5% confident that the true proportion of actors who areextroverts falls above this interval.We are 5% confident that thetrue proportion of actors who are extroverts falls within thisinterval.    We are 95% confident that the trueproportion of actors who are extroverts falls within thisinterval.We are 95% confident that the true proportion of actorswho are extroverts falls outside this interval.
(c) Do you think the conditions np > 5 and nq> 5 are satisfied in this problem? Explain why this would be animportant consideration.
No, the conditions are not satisfied. This is important becauseit allows us to say that p̂ is approximately normal.No,the conditions are not satisfied. This is important because itallows us to say that p̂ is approximatelybinomial.    Yes, the conditions are satisfied.This is important because it allows us to say that p̂ isapproximately normal.Yes, the conditions are satisfied. This isimportant because it allows us to say that p̂ isapproximately binomial.
