A sample of size 100 is selected from a population with p = .40. a. What is the expected value of p(bar)?
b. What is the standard error of p(bar)?
c. Show the sampling distribution of p(bar)?
d. What does the sampling distribution of p show?

(a) 0.40

(b) 0.049

(c)

(d) Explained below

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

The standard deviation of this sampling distribution of sample proportion is:

Given:

n = 100

p = 0.40

As n = 100 > 30 the Central limit theorem is applicable.

(a)

Compute the expected value of as follows:

The expected value of is 0.40.

(b)

Compute the standard error of as follows:

The standard error of is 0.049.

(c)

The sampling distribution of is:

(d)

The sampling distribution of p show that as the sample size is increasing the distribution is approximated by the normal distribution.