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 img 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) equation

is distributed as img. Moreover, it can be shown that

img

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

img

img

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

(13.21)

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

Get Statistical Inference: A Short Course now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.