# Interval Estimation

• Dec 12th 2008, 10:09 AM
Sameera
Interval Estimation
Q: A random sample of size 15 from a population which is n( μ, σ2 )
yields
=3.2 and S^2=4.24 Find 90% confidence interval for σ2.

I know confidence interval for σ2 is [ns^2/b, ns^2/a]

but how values to determine a and b??? in my book they have assign a=6.57 and b=23.7
BUT HOW??? please tell .. i have to try another question of same type ...

thanks .........!!
• Dec 12th 2008, 11:58 AM
CaptainBlack
Quote:

Originally Posted by Sameera
Q: A random sample of size 15 from a population which is n( μ, σ2 )
yields
=3.2 and S^2=4.24 Find 90% confidence interval for σ2.

I know confidence interval for σ2 is [ns^2/b, ns^2/a]

but how values to determine a and b??? in my book they have assign a=6.57 and b=23.7
BUT HOW??? please tell .. i have to try another question of same type ...

thanks .........!!

$\displaystyle ns^2$ is the sum of the squares of $\displaystyle 15$ normally distributed RV's (almost as we are estimating the mean from the sample, so we in practice have one less degree of freedom). This has a $\displaystyle \chi^2$ distribution with $\displaystyle \nu=14$, and your values of $\displaystyle a$ and $\displaystyle b$ come from the $\displaystyle \chi^2$ tables. (your confidence interval is a $\displaystyle 90\%$ interval)

CB