## STAT 303, 503-504, Spring 1996 Prof. H. Joseph Newton Outline of Lecture 25

1. The Minimum Variance Estimation Concept Lab.
2. The pooled estimate of variance for independent samples from normal populations having equal variances.
3. The pooled estimate of 0-1 population proportion from two independent samples from the population.
4. 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.
5. 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.