1. 7.5 Hypothesis Testing for Variance and Standard Deviation Key Concepts: –The Chi-Square Distribution –Critical Values and Rejection Regions –Chi-Square Test for σ 2 and σ

2. 7.5 Hypothesis Testing for Variance and Standard Deviation We built confidence intervals for σ 2 and σ in the last chapter. –If our variable of interest was normally distributed, then a modified version of the sample standard deviation s 2 followed a chi-square distribution with n-1 degrees of freedom.

3. 7.5 Hypothesis Testing for Variance and Standard Deviation Without technology, it is difficult to calculate the p-values of a variable that follows a chi-square distribution. –We will use the critical-value approach in these tests. Practice finding critical values: #6 p. 400 (right-tailed test) #10 (two-tailed test)

4. 7.5 Hypothesis Testing for Variance and Standard Deviation How can we use what we learned in chapter 6? –If our variable of interest is normally distributed, the modified version of s 2 will serve as our ‘standardized’ test statistic: –We can use this when testing for both σ 2 and σ. We need to make sure to use the chi-square distribution with n-1 degrees of freedom when we run our tests. –Guidelines for this chi-square test are provided on page 396.

5. 7.5 Hypothesis Testing for Variance and Standard Deviation Practice testing for a population variance #18 p. 401 (Gas Mileage) Practice testing for a population standard deviation #22 p. 401 (Hotel Room Rates)