Question

In a random sample of 63 professional actors, it was found that 45 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 above 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 within this interval.We are 95% confident that the true proportion of actors who are extroverts falls within 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 p̂ is approximately binomial.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 normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

Answer 1

Answer:

Given Data

X = 45

n = 63

So,

a)

Let p represent the proportion of all actors who are extroverts. Find a point estimate for p.

= 0.7143

b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit         
upper limit       

At 95% confidence interval the z is

= 5%

= 0.05

= 1.96

At 95% confidence interval for p is

Lower limit = 0.602776

Upper limit = 0.825824

We are 95% confident that the true proportions of actors who are extravoters falls within 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 p̂ is approximately normal.

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