Question

Consider a sampling distribution with p=0.09 and samples of size n each. Using the appropriate​ formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion.

a. For a random sample of size n=4000.

b. For a random sample of size n=1000.

c. For a random sample of size n=250.

Answer 1

A)

As per the given information

mean μp^=p= 0.09

random sample size n=4000

standard deviation σp^ = Sqrt( p (1-p) /n)

=sqrt( 0.09 * 0.91 / 4000)

=0.004524

B)

mean μp^=p= 0.09

random sample size n=1000

standard deviation σp^ = Sqrt( p (1-p) /n)

=sqrt( 0.09 * 0.91 / 1000)

=0.00904

C)

mean μp^=p= 0.09

random sample size n=250

standard deviation σp^ = Sqrt( p (1-p) /n)

=sqrt( 0.09 * 0.91 / 250)

=0.01809