Question

A population has parameters μ=121.3μ=121.3 and σ=57.7σ=57.7. You intend to draw a random sample of size n=160n=160.

What is the mean of the distribution of sample means?
μ¯x=μx¯=

What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σ¯x=σx¯=

You intend to draw a random sample of size n=636n=636 from a population whose parameter is p = 0.40133333333333
What is the mean of the distribution of sample means?
μˆp=μp^=  

What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σˆp=σp^=

Answer 1

$\mu_{\bar{x}}=\mu=121.3\\ \sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=4.56,~where~n=160\\ \mu_{\hat{p}}=p=0.40133333333333\\ \sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}=0.02~where,~n=636$