Question

Which of the following statement about the sampling distribution of proportion is true? Select one: a....

Which of the following statement about the sampling distribution of proportion is true?

Select one:

a. Its mean equals to the population proportion.

b. Its standard error equals to the population standard deviation.

c. It is approximately normally distributed if n ≥ 30.

d. It is approximately normally distributed if the population is normally distributed.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution:

Correct option is

a. Its mean equals to the population proportion.

Explanation:

We have to discuss the sampling distribution of proportion , not mean.

Let p be the population proportion.

n be the sample size.

Let be the sample proportion.

The sampling distribution of is approximately normal with

mean = =  p

SD =   =     

The necessary condition for the distribution is to be normal is that ,

n * p and n* (1 - p) both are 10

Correct option is

a. Its mean equals to the population proportion.

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