# Sampling Distribution

• Nov 1st 2012, 10:55 PM
rokman54
Sampling Distribution
Hi.

I'm having a little problem solving this one.

Let X(bar) and S^2 denote the sample mean and sample variance in random sampling, sample size 20 from a N(10,80) distribution population. Calculate the probabilities of the following events.

10<= X(bar) <= 12, S^2 <= 108.8

Z= (X(bar)-10/(root(80/20))

Since X(bar) ~ (u, sigma^2/n), 10-10/(root(80/20) <= Z <= 12-10 / (root(80/20)

0 <= Z<= 1

19S^2/80 <= 10.8*19/80 ~ Chi-square (19)

Now how do I find the common area between the two events?

Also how should I approach

X(bar) <= 10 + 0.2037S

Thanks.
• Nov 1st 2012, 11:41 PM
chiro
Re: Sampling Distribution
Hey rokman54.

X_bar and S^2 should be independent so there will be nothing in common between the those two events. If there is then you can't use the common distributional assumptions (like a t-test for example).

If X_bar and S^2 are dependent on each other than you should not have a Normal distribution (in relation to the same way that mu and sigma^2 are independent parameters).
• Nov 2nd 2012, 08:42 AM
rokman54
Re: Sampling Distribution
Thanks.

Also I figured out how to do the second : a simple t distribution.