Question

Describe the sampling distribution of p. Assume the size of the population is 25,000. n=700​, p=0.3

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Choose the phrase that best describes the shape of the sampling distribution of p (hat) below.

A.Not normal because n≤0.05N and np(1−p)≥10.

B.Approximately normal because n≤0.05N and np(1−p)<10.

C.Approximately normal because n≤0.05N and np(1−p)≥10.

D.Not normal because n≤0.05N and np(1−p)<10.

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Determine the mean of the sampling distribution of p.

μp=___ ​(Round to one decimal place as​ needed.)

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Determine the standard deviation of the sampling distribution of p.

σp=__ ​(Round to three decimal places as​ needed.)

Answer 1

5% of population is = 25000 * 0.05 = 1250

The sample size is = 700

p = 0.3

np(1-p) = 700 * 0.3 * 0.7 = 147 which is greater than 10.

The sampling distribution of is approximately normal because   and .

option C is correct.

The mean of the sampling distribution of is the same as the population proportion.

The standard deviation of the sampling distribution of is

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