Reference no: EM132856050

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 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. which one?

We are 5% 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.

We are 95% 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.

(c) Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? which one?

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