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"Thirty percent of U.S. adults say they prefer cats" . a. random sample of size n=20...

"Thirty percent of U.S. adults say they prefer cats" .

a. random sample of size n=20 US adults is selected . find the mean and the standard deviation of the distribution of sample proportions according to the Central Limit Theorem for proportions.

b. random sample of size n=200 US adults is selected.find mean and the standard deviation of the distribution of sample proportions according to the Central Limit Theorem for proportions.

c. in either a or b, is the distribution of sample proportions to be closer to a Normal approximation and why?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a)

Mean = = 0.30

Standard deviation = sqrt[ ( 1 - ) / n] = sqrt [ 0.3 * ( 1 - 03) / 20] = 0.1025

b)

Mean = = 0.30

Standard deviation = sqrt[ ( 1 - ) / n] = sqrt [ 0.3 * ( 1 - 03) / 200] = 0.0324

c)

Since sample size for b is sufficiently large and both conditions

n >= 10 and n ( 1 - ) >= 10 for part b.

For b, the distribution of sample proportions to be closer to a Normal approximation

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