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86: Testing a claim about a standard deviation or variance
In section 7.5 we used the chisquare distribution to help us construct confidence
intervals about the population variance and standard deviation.
Here, we will use
the chisquare distribution to perform hypothesis test about the population
standard deviation σ.
Recall the following from section 7.5.
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.
Just like our hypothesis tests about the population mean and the population
proportion, there are three forms for the hypothesis test about the population
standard deviation σ. The notation σ
0
refers to the value of σ to be tested.
Form
Null and alternative hypotheses
Righttailed test, onetailed test
H
0
: σ
σ
0
H
1
: σ >
σ
0
_____________________________________________________________________________________________
Lefttailed test, onetailed test
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This note was uploaded on 04/16/2010 for the course MATHEMATIC 1231 taught by Professor Driscoll during the Spring '10 term at Clayton College of Natural Health.
 Spring '10
 Driscoll
 Statistics, Standard Deviation, Variance

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