Confidence Interval for the Variance of a Normal Distribution
In practice, though a population may have a 'true' value for thevariance, this is never know and the variance is always estimatedfrom a sample using the formulaWecan use this to find a confidence interval for the unknownvarianceofwhichisan estimate.
We can do this using the fact thatthedistributionwithdegrees of freedom.
Denoting byandtheupper and lowerpointsof thedistributionwithdegreesof freedom we have thatwitha certainty of
We can separate this into two inequalities:
We can combine these two into a single inequalitywitha certainty ofTheconfidence interval is
Example: The standard deviation of a sample of 15 tomato plants is5.8 cm. Find a 95% confidence interval for the variance of the tomatoplant population.
The upper and lower 2.5% points of the %chi^2 distribution with(15-1)=14 degrees of freedom are 5.63 and 26.12 respectively. Theconfidence interval is