In a random sample of 62 professional actors, it was found that 37 were extroverts.
(a) Letp represent the proportion of all actors who are extroverts. Find a point estimate forp. (Round your answer to four decimal places.)
(b) Find a 95% confidence interval forp. (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 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.
We are 5% confident that the true proportion of actors who are extroverts falls above this interval.
We are 5% confident that the true proportion of actors who are extroverts falls within this interval.
(c) Do you think the conditionsn·p > 5 andn·q > 5 are satisfied in this problem? Explain why this would be an important consideration.
No, the conditions are not satisfied. This is important because it allows us to say thatp̂ is approximately normal.
No, the conditions are not satisfied. This is important because it allows us to say thatp̂ is approximately binomial.
Yes, the conditions are satisfied. This is important because it allows us to say thatp̂ is approximately binomial.
Yes, the conditions are satisfied. This is important because it allows us to say thatp̂ is approximately normal.