# Confidence inteval

• Jan 30th 2010, 06:47 AM
Pinto9
Confidence inteval
Let X be a random variable following a normal distribution.
A sample is taken from a population.
If n= 8
sample mean = 7.2

(i=1) E (n=8) [x(i) - x-bar ]^2 = 3.44

Calculate a 99% confidence interval for the population standard deviation?

Do you do this by first solving for the population variance confidence interval and then taking the square root of the upper and lower limits?
• Jan 30th 2010, 07:44 AM
matheagle
Is that E really a sum?
You need to use the chi-square distribution for a CI about sigma.
• Jan 30th 2010, 10:25 AM
Pinto9
Quote:

Originally Posted by matheagle
Is that E really a sum?
You need to use the chi-square distribution for a CI about sigma.

Yes, E = sum.

You mean the confidence interval is
(n-1)s^2/ X^2 (n-1);(a/2)

and

(n-1)s^2/ X^2 (n-1);(1 - a/2)?

Like (3.44/20.28 ; 3.44/0.989)?

But I thought the standard deviation CI was being asked for, not the variance CI, or could you maybe explain how this works? Thanks!
• Jan 30th 2010, 03:09 PM
matheagle
I didn't check your CI formula
BUT IF (a,b) is your CI for $\sigma^2$
Then $(\sqrt{a},\sqrt{b})$ is the CI for $\sigma$
• Jan 31st 2010, 04:54 AM
Pinto9
Quote:

Originally Posted by matheagle
I didn't check your CI formula
BUT IF (a,b) is your CI for $\sigma^2$
Then $(\sqrt{a},\sqrt{b})$ is the CI for $\sigma$

Ok, thanks!