Answer:
(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 <em>n</em> = 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.