Inference about Variances
Sampling Distribution of Variances
:
You want to know the variance of a population.
But you realize
the population is too large to actually compute the true variance.
So you decide to observe a sample from the population and use the
sample variance as an estimate of the population variance.
You
need the sampling distribution of the sample variance in order to
make inference about the population variance.
The population is normally distributed with mean
μ
and standard
deviation
σ
.
Let
y
denote an observation from the population.
Draw sample of size n
→
.
12
,,
n
yy
y
K
Compute the
sample
variance
2
2
()
1
i
i
s
n
−
=
−
∑
.
Then sampling distribution of
(n1)s
2
/
σ
2
is chisquare with n1
degrees of freedom.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentInference about Variances
Use the table for the chisquare distribution or a computer program
to get probabilities.
Examples:
Suppose
X
has chisquare distribution with df=4.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '08
 Staff
 Normal Distribution, Variance, Nf, 1 degrees, 0.470 nm

Click to edit the document details