# Finding sample standard deviation

• Mar 8th 2010, 06:45 PM
jass10816
Finding sample standard deviation
If a 90% confidence interval for $\sigma^2$ is reported to be (51.47,261.90), what is the value of the sample standard deviation.

Attempt:
$51.47<\sigma^2<261.90$

So
$\frac{(n-1)s^2}{\chi_{.95,n-1}^2}=51.47$ and $\frac{(n-1)s^2}{\chi_{.05,n-1}^2}=261.90$

Then
$s=\sqrt{\frac{51.47*\chi_{.95,n-1}^2}{n-1}}=\sqrt{\frac{261.90*\chi_{.05,n-1}^2}{n-1}}$

$5.0884=\frac{\chi_{.95,n-1}^2}{\chi_{.05,n-1}^2}$

So this looks like it should have an F-distribution with same numerator and denominator degrees of freedom, which should help me figure out what those degrees of freedom are.

I can't figure out how to do this. Or am I way off?
• Mar 8th 2010, 09:39 PM
matheagle
you need n, and then just look up either of those chi-square percentiles
then solve for s.
If, you really don't have n, just go down the tables and see which of those ratio of percentiles
Which F-Distribution table should I use? In other words, how do I infer the alpha level from my work so far? Is it just the same as for $\sigma^2$, which is .10?