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 40 were extroverts.
(a)Let p represent the proportion of all actors who are extroverts. Find a point estimate for p.
(b)Find a 95% confidence interval for p.Give a brief interpretation of the meaning of the confidence interval you have found.
(c)Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.
a)
Sample proportion
= 40 / 65 = 0.615
b)
95% confidence interval for p is
- Z
/2
* Sqrt [
( 1 -
)/ n] < p <
+ Z
/2
* Sqrt [
( 1 -
)/ n]
0.615 - 1.96 * sqrt [ 0.615 * (1 - 0.615) / 65] < p < 0.615 + 1.96 * sqrt [ 0.615 * (1 - 0.615) / 65]
0.497 < P < 0.733
Interpretation -
We are 95% confident that true proportion of all actors who are extroverts are between 0.497 and 0.733
c)
np = 0.615 * 65 = 40 . 5
nq = 65 * ( 1 - 0.615) = 25 > 5
Both conditions are satisfied.
This is important, since both conditions are satisfied, the sampling distribution of proportion is
approximately normal.
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to ro...
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 35 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 ...
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 41 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 ...
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 63 professional actors, it was found that 36 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 ...
QUESTION # 1 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 66 professional actors, it was found that 39 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...
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 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.)
lower limit
upper limit
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