We
can use this to find a confidence interval for the unknown
variance
of
which
is
an estimate.
A Level Maths Notes: S4 – Confidence Interval for the Variance of a Normal Distribution
In practice, though a population may have a 'true' value for the
variance, this is never know and the variance is always estimated
from a sample using the formulaWe
can use this to find a confidence interval for the unknown
varianceof
whichis
an estimate.
We can do this using the fact that
the
distribution
with
degrees of freedom.
Denoting by
and
the
upper and lower
points
of thedistribution
withdegrees
of freedom we have that
with
a certainty of
We can separate this into two inequalities:
We can combine these two into a single inequality
with
a certainty ofThe
confidence interval is
Example: The standard deviation of a sample of 15 tomato plants is 5.8 cm. Find a 95% confidence interval for the variance of the tomato plant 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. The confidence interval is
