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8 6 Testing a claim about a standard deviation or variance In section 7 5 we used the chi square distribution to help us construct confidence intervals about the population variance and standard deviation Here we will use the chi square distribution to perform hypothesis test about the population standard deviation Recall the following from section 7 5 2 chi square distribution Suppose we take a random sample of size n from a normal population with mean and standard deviation Then the sample statistic follows a 2 distribution with n 1 degrees of freedom where s2 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 The notation 0 refers to the value of to be tested Form Right tailed test one tailed testH0 Null and alternative hypotheses 0 H 1 0 Left tailed test one tailed test H 0 0 H 1 0 Tow tailed test H 0 0 H 1 0 Under the assumption that H0 is true the chi square statistic takes the following form For the hypothesis test about the test statistic is This test statistic takes a moderate value when the value of s2 is moderate assuming H0 is true and the test statistic takes an extreme value when the value of s2 is extreme assuming H0 is true This leads us to the following When the observed value of is unusual or extreme on the assumption that H0 is true we should reject H0 Otherwise there is insufficient evidence against H0 and we should not reject H0 Critical values and rejection rules for the chi square test for Form Null and alternative hypotheses Right tailed test one tailed testH0 0 H 1 0 Critical value Reject H0 if left tailed test one tailed test H0 0 H 1 0 Critical value Reject H0 if two tailed test H 0 0 H 1 0 Critical values Reject H0 if Guideline for chi square test for using the traditional method This hypothesis test is valid only if we have a random sample from a normal population Step1 State the



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