## STAT 303, 503-504, Spring 1996

Prof. H. Joseph Newton

Outline of Lecture 25

- The Minimum Variance Estimation Concept Lab.
- The pooled estimate of variance for independent
samples from normal populations having equal variances.
- The pooled estimate of 0-1 population proportion
from two independent samples from the population.
- Comparing means and variances using confidence
intervals:
- A confidence interval can be thought of as a set of
reasonable values for a parameter.
- Two variances are equal, if and only if, their ratio
is 1. Thus, it is reasonable to conclude that two variances
are equal if 1 is in the confidence interval for their ratio.
- Two means are equal, if and only if, their difference
is 0. Thus, it is reasonable to conclude that two means
are equal if 0 is in the confidence interval for their difference.

- I am 100(1-alpha)% confident that the true value of the parameter
is contained in the confidence interval I calculated
because statistical theory says
(and the Interpreting Confidence Intervals Concept Lab illustrates)
that if I calculated the CI many many times for different samples (or pairs
of samples for the two sample cases), then 100(1-alpha)% of the time, the
true value of the parameter would be in the interval.