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 69 professional actors, it was found that 36 were...

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 69 professional actors, it was found that 36 were extroverts.

(a)

Letp represent the proportion of all actors who are extroverts. Find point estimates forp andq. (Round your answer to four decimal places.)

p̂=

q̂=

(b) Find a 95% confidence interval for
p.

Find the maximal margin of error. (Round your answer to two decimal places.)

E =

Report the bounds from the 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 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 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
np > 5 andnq > 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 p̂ is approximately normal.

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

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

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

Jun 08, 2022

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