Assume that each sample is obtained by randomly selecting values from a population with a normal distribution. In constructing confidence intervals for Ï or Ï2,

Assume that each sample is obtained by randomly selecting values from a population with a normal distribution.
In constructing confidence intervals for σ or σ2, we use Table A-4 to find the critical values x2L and x2R, that table applies only to cases in which n ‰¤ 101, so the number of degrees of freedom is 100 or fewer. For larger numbers of degrees of freedom, we can approximate x2L and x2R by using

where k is the number of degrees of freedom. Construct the 95% confidence interval for σ by using the following sample data: The measured heights of 772 men between the ages of 18 and 24 have a standard deviation of 2.8 in.

+ V2k - 1