For this problem, carry at least four digits after the decimal in your calculati
ID: 3063639 • Letter: F
Question
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 65 professional actors, it was found that 42 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.)
(c) 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 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.
(d) Do you think the conditions np > 5 and nq > 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 normal.
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 binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial.
Explanation / Answer
The statistical software output for this problem is:
One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald
95% confidence interval results:
Hence,
a) Point estimate for p = 0.6462
b) 95% confidence interval: (0.53, 0.76)
c) We are 95% confident that the true proportion of actors who are extroverts falls within this interval. Option A is correct.
d) Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. Option A is correct.
Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 42 65 0.64615385 0.059308717 0.5299109 0.7623968Related Questions
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