7.5 Hypothesis Testing for Variance and Standard Deviation

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 s2 and s

2
7.5 Hypothesis Testing for Variance and
Standard Deviation

• We built confidence intervals for s2 and s in
  the last chapter.
• If our variable of interest was normally
  distributed, then a modified version of the
  sample standard deviation s2 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 s2 will
  serve as our standardized test statistic
• We can use this when testing for both s2 and s.
• 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)