Condence Interval for a Population Variance For use with

Chapter 8, Problem 8.6.10

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Condence Interval for a Population Variance For use with 8.6.118.6.14.Recall that if the data observations are normally distributed, then the sample variance S2 has the distribution S2 2 2 n1 n1 (a) Show that this result implies that P2 1/2,n1 (n1)S2 2 2 /2,n1=1 (b) Deduce that P(n1)S2 2 /2,n1 2 (n1)S2 2 1/2,n1=1 so that (n1)s2 2 /2,n1 , (n1)s2 2 1/2,n1 is a 1 level two-sided condence interval for the population variance 2. (c) Explain why (n1)s2 2 /2,n1 ,(n1)s2 2 1/2,n1is a 1 level two-sided condence interval for the population standard deviation .Even though the population mean is usually the parameter of primary interest to an experimenter, in certain situations it may be helpful to use this method to construct a condence interval for the population variance 2 or population standard deviation . An unfortunate aspect of these condence intervals is that they depend heavily on the data being normally distributed, and they should be used only when that is a fair assumption. You may be able to obtain these condence intervals on your computer package.