Thread: sampling distribution

Originally Posted by chrisc

Hello
I'm working on a homework question and I am looking for some assistance.
The question refers back to another, but I believe this is all the information below.

n = 20
variance = 1.4
let S^2 denote the sample variance of the 20 measurements

a) find b such that P(S^2 < b) = .975
b) find a such that P(a < S^2) = .975

the answers are given in the back, which are
a) 2.42
b) 0.656

You need to know the distribution of the sample variance. Click on 6.1 at this link: Variance - Wikipedia, the free encyclopedia

Post in this thread if you're still stuck (show you're working and say where you're stuck).

ah thank you
i figured it out.
it may sound stupid, but i kept leaving out the important step of diving by the variance

there was a part (c) i left out because those first two were priority in order to start this question.

c) If a and b are as in parts (a) and (b), what is P(a < S^2 < b)?
the answer is 0.95

It is because both values cut off an area of 0.025 each, so together they would cut off 0.05, which 1-0.05=0.95?

or is there a more complicated math to it?

Originally Posted by chrisc

ah thank you
i figured it out.
it may sound stupid, but i kept leaving out the important step of diving by the variance

there was a part (c) i left out because those first two were priority in order to start this question.

c) If a and b are as in parts (a) and (b), what is P(a < S^2 < b)?
the answer is 0.95

It is because both values cut off an area of 0.025 each, so together they would cut off 0.05, which 1-0.05=0.95?

or is there a more complicated math to it?

Yes. If you draw a rough sketch of the pdf and shade the required area the reason is obvious.