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 of the following parts:

A)for random sample of size n=5000

B)for random sample of size n=1000

C)for random sample of size n=500

Answer 1

Mean of sampling distribution od sample proportion = $\mu$_$\hat{p}$

Standard deviation of sampling distribution of sample proportion = $\sigma$_$\hat{p}$

A)

$\mu$_$\hat{p}$ = p = 0.09

$\sigma$_$\hat{p}$ = Sqrt( p ( 1 -p) / n)

= Sqrt(0.09 * 0.91 / 5000)

= 0.00405

B)

n= 1000

$\mu$_$\hat{p}$ = p = 0.09

$\sigma$_$\hat{p}$ = Sqrt( p ( 1 -p) / n)

= Sqrt(0.09 * 0.91 / 1000)

= 0.00905

C)

n = 500

$\mu$_$\hat{p}$ = p = 0.09

$\sigma$_$\hat{p}$ = Sqrt( p ( 1 -p) / n)

= Sqrt(0.09 * 0.91 / 500)

= 0.01280