Statistical Inference: A Short Course

13.8 A Confidence Interval for σ² Under Random Sampling from a Normal Population

Let us first discuss the properties of the sampling distribution of the sample variance when sampling from a population that is normally distributed. Specifically, if s² is determined from a sample of size n taken from a normal population with mean μ and variance σ², then the quantity

(13.20)

is distributed as . Moreover, it can be shown that

Then given Equation (13.20), it follows that and that

For Y defined above, we seek to determine quantiles and such that

(13.21)

(Fig. 13.2). Upon transforming Equation ...