Section 7.5
HYPOTHESIS TESTING
FOR VARIANCE AND
STANDARD DEVIATION
Uses the Chi-Square Test
To find critical value(s)
 1. Specify level of significance, α
 2. Find degrees of freedom
 3. Use the Chi-Square table. (#6)
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◦ For a right tailed test, use α
◦ For a left tailed test, use (1 – α)
◦ For a 2-tailed test, use ½α and (1 – ½α)
Find the critical value(s)
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Right tailed test, α = 0.10, n = 10
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Left tailed test, α = 0.05, n = 24
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Two tailed test, α = 0.01, n = 61
Finding the Test Statistic
Guidelines for the X2 -Test
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1. find H0 and Ha
2. identify α
3. find the critical value(s)
4. shade the rejection region(s)
5. find X2
6. make decision to reject or not
reject the null hypothesis
7. interpret decision in context

An auto manufacturer believes that
the variance of the gas mileages of
its hybrid vehicles is 1.0. You work
for an energy conservation agency
and want to test this claim. You find
that a random sample of the gas
mileages of 25 of the manufacturer’s
hybrid vehicles has a variance of
1.65. At α = 0.05, do you have
enough evidence to reject the
manufacturer’s claim?

A state school administrator says
that the standard deviation of test
scores for 8th grade students who
took a US history test is greater
than 30 points. You work for the
administrator and are asked to test
this claim. You randomly select 18
tests and find the standard deviation
to be 30.6 points. At α = 0.01, is
there enough evidence to support
the administrator’s claim?