Consistency of Stratified Random Sampling Estimators in Repetive Sampling

This study focuses on consistency of stratified random sampling in repeated sampling processes within a population with heterogeneous characteristics. The data for the study is a real life data on number of students in schools where the stratification is on the basis of ownership (public or private). Proportional allocation method was used to determine the number of units (schools) to be chosen from each stratum for a given sample size and four (4) independent samples of equal sample sizes were chosen and estimates of mean ,variance as well as confidence interval obtained with the estimators of stratified random sampling. The estimates obtained for each sample sizes were subjected to a test of significance to test the null hypothesis of no significance difference between the estimates and the actual value using the t-statistic. The analysis revealed that the estimates obtained for different samples differs but the test of significance revealed that there is no significant difference in the estimates across the independent samples as the P-values are less the level of significance   0.05 except for n  30 which could be considered as an outlier. Also, there is no significant difference in the estimates of variances for the various sample sizes considered for this study with a Pvalue of 0. 2344.