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Lower tail or two tailed Chi-square tests

 

 

Example

A brand new air conditioner from Carrier must maintain the selected temperature with little variation.  Specifications from the company call for a standard deviation of not more than 2 degrees (or variance of 4 degrees2).  A sample of 4 air conditioners is tested and yields a sample variance of s2 = 6.  Test to see whether the standard deviation specification is exceeded.
Use
α = 0.05.
 

Solution

The chi-square table to find the critical value:
χ2α = 7.815 (α = 0.05 and (4 – 1) = 3 d.f.)
 
The test statistic is:



There is not significant evidence at the α = 0.05 level that the standard deviation specification is exceeded
 

 





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