Combining independent normal Sample means by weighting With their standard errors

The problem of estimating the common mean of several normal populations based on independent samples available from all the populations is considered. Two combined estimators are compared. One is the weighted average of the individual sample means with weights inversely proportional to their estimated standard errors and another is the traditional one which combines the individual sample means with weights inversely proportional to their estimated variances . Exact expressions for the variances of and are derived. These estimators are compared numerically with respect to their variances. Comparison studies indicate that is superior to if the sample sizes are small and/or the population variances are not far apart from each other. Further,applications of these point estimates and the confidence intervals centered at these estimates to practical examples are discussed.