Ch 8 Sec 5

# Ch 8 Sec 5 - Chapter8Section5 TestforaVarianceora...

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Chapter 8 Section 5 Test for a Variance or a  Standard Deviation Mr. Kenneth Horwitz

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Test for a Variance or a  Standard Deviation The chi-square distribution is also used to test a claim about a  single variance or standard deviation.      The formula for the chi-square test for a variance is with degrees of freedom d.f. =  n  – 1 and n  = sample size s 2 = sample variance s 2 = population variance ( 29 2 2 2 1 - = n s χ σ 2
Assumptions for the      Test for a  Variance or a Standard Deviation 1. The sample must be randomly selected from the  population. 2. The population must be normally distributed for  the variable under study. 3. The observations must be independent of one  another. 2 χ

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Table G Find the critical chi-square value for 15 degrees of freedom  when  α = 0.05 and the test is right-tailed. 2 24.996 = χ
Example 2: Table G Find the critical chi-square value for 10 degrees of freedom  when  α = 0.05 and the test is left-tailed. When the test is left-tailed, the  α  value must be subtracted  from 1, that is, 1 – 0.05 = 0.95. The left side of the table is  used, because the chi-square table gives the area to the right of  the critical value, and the chi-square statistic cannot be  negative.

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Ch 8 Sec 5 - Chapter8Section5 TestforaVarianceora...

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