The Least Sample Sizes for Interval Estimation of the Difference between the Means of Two Populations

Abstract

The objective of this research is to find the least sample sizes for interval estimation of thedifference between the means of two populations using z and t statistics. Populations specified inthis research are symmetry and non-symmetry distributions. In order to obtain the sample sizes,confidence coefficients estimation (1 - α^ ) are compared with the specified confidence coefficients(1 - α): 0.90, 0.95 and 0.99. When 1 - α^ is significantly equal to 1 - α , then the sample sizes isappropriate. This research used the Monte Carlo Simulation method. The experiment was repeated10,000 times for each condition. Results of the study are as follows:

When the population has symmetry distribution, the least sample sizes that cover all casesare n1 ≥ 17 and n2 ≥ 30 . When the population has positively skewed distribution, the minimumsample sizes that cover all cases are n1 ≥ 18 and n2 ≥ 40. When the population has negativelyskewed distribution, the minimum sample sizes that cover all cases are n1 ≥ 17 and n2 ≥ 42.