7.5 Estimating a Population Variance
We have seen how confidence intervals can be used to estimate the unknown
value of a population mean or a proportion.
We used the normal and student t
distributions for developing these estimates. However, the variability of a
population is also important. As we have learned, less variability is almost always
better. We use the chisquare distribution (pronounce as kighsquare) to
construct the confidence intervals (estimates) of variances or standard deviations.
First we n
eed to become acquainted with the χ
2
distribution.
χ
2
(chisquare) distribution
Suppose we take a random sample of size n from a normal population with mean
µ and standard deviation σ. Then the sample statistic
follows a
χ
2
distribution with n1 degrees of freedom, where
s
2
represents the sample
variance.
Properties of the
χ
2
(chisquare) distribution
The total area under χ
2
curve equals 1.
The value of the χ
2
random variable is never negative, so the χ
2
curve starts
at 0. However, it extends indefinitely to the right, with no upper bound.
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 Spring '10
 Driscoll
 Statistics, Normal Distribution, Variance, Honda Accord, Chisquare distribution, Ford Escape, Lexus RX

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