Test of significance of the difference between means of two small samples drawn
from the same normal population
Let and be the sample means for two small samples drawn from a normal
population. The test statistics is
The degrees of freedom is
M
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Significance Testing for Differences in Means of Small Samples, Summaries of Probability and Statistics
Two statistical tests for determining the significance of the difference between means of two small samples drawn from the same or different normal populations. The first test is for samples drawn from the same normal population, while the second test is for samples drawn from different normal populations with potentially different means. The test statistics, degrees of freedom, and critical points for each test. It also includes a practical example of comparing the average life of two types of batteries, as well as a problem involving testing the equality of means for two samples of nicotine content in tobacco. Important concepts in statistical inference, hypothesis testing, and the analysis of small sample data from normal distributions, which are relevant for students and researchers in fields such as statistics, data analysis, and experimental design.
Typology: Summaries
2023/2024
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Test of significance of the difference between means of two small samples drawn from the same normal population Let and be the sample means for two small samples drawn from a normal population. The test statistics is The degrees of freedom is M
Test of significance of the difference means of two small samples drawn from the normal populations having different mean values Let and be the sample means for two small samples drawn from the normal population with means and. The test statistics is and the degrees of freedom is Critical points: (^) Where ଶ భ௦భ మ ାమ௦మ మ భାమ ି ଶ . or (For pooled)
Under null hypotheses (^) : where is the pooled standard deviation given by, ୮ ଶ ଶ ଶ ଶ The value of is calculated for the given information as