Reference no: EM132465069
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 67 professional actors, it was found that 36 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.
We are 5% confident that the true proportion of actors who are extroverts falls within this interval.
We are 5% confident that the true proportion of actors who are extroverts falls above this interval.
We are 95% confident that the true proportion of actors who are extroverts falls within this interval.
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.
Yes, the conditions are satisfied. This is important because it allows us to say that p^ is approximately binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p^ is approximately binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p^ is approximately normal.
Yes, the conditions are satisfied. This is important because it allows us to say that p^ is approximately normal.
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