ช่วงความเชื่อมั่นสำหรับค่าเฉลี่ยร่วมของ 2 กลุ่มประชากรที่มีการแจกแจงปกติ / ธนภัทร ศรภักดี = Confidence intervals for the common mean of two normal populations / Tanaphat Sornphakdee
The objective of the study is to compare the interval estimation methods for mean of two normal populations under which unequal variances is considered. The comparison of average confidence interval lengths will be compared in case of the confidence coefficients of interval estimation methods are equal to the given confidence coefficient value. The estimation method having the shortest average confidence interval length is considered to be optimum estimation method. The estimation methods under consideration in this study are the interval estimation method with absolute maximum of t-statistics, the interval estimation method with linear combination of t-statistics and the interval estimation method with linear combination of F-statistics. The methods are compared under two patterns of the ratio of variances (σ 21: σ2₂) that the first population variances is less than the second populations variances (σ 21 < σ2₂) and the first populations variances is larger than the second populations variances (σ 21 > σ2₂). Three different ratio of variances are considered: small (1:1.5,1:2.5,1:3.5), medium (1:4.5,1:5.5,1:6.5) and large (1:7.5,1:10,1:15). The equal sample sizes are 10,20,30 and 50, respectively. The unequal sample sizes (n1, n2) are (10,15), (10,20), (10,30), (15,30), (20,25), (20,30), (20,40), (20,60), (30,45), (40,50), (40,60), (40,80) and (60,75), respectively. The given confidence coefficient value is 0.95. The experimentation data are generated by the Monte Carlo Simulation technique. Each simulation consists of 2000 runs. The conclusions of this study are as follows: 1. The confidence coefficients of all interval estimation methods are equal to the given confidence coefficient value. 2. All cases of sample sizes(n1, n2) 1 the average confidence interval length of the interval estimation method with linear combination of t-statistics(Ct) is shortest in situation where the first populations variances is less than the second populations variances ( σ 21 < σ2₂ ) and where the first populations variances is little larger than the second populations variances (σ 21 > σ2₂ ) ,whereas the unequal sample sizes are much difference and the first sample sizes are small (n1≤20), average confidence interval length of the interval estimation method with linear combination of F-statistics(CF) is shortest , when one of variances is much larger than the other. The average confidence interval length varies according to the ratio of variances but varies inversely with sample sizes.
