HYPOTHESIS TESTING FOR DIFFERENCES BETWEEN MEANS - Research Methodology

In many decision-situations, we may be interested in knowing whether the parameters of two populations are alike or different. For instance, we may be interested in testing whether female workers earn less than male workers for the same job. We shall explain now the technique of hypothesis testing for differences between means. The null hypothesis for testing of difference between means is generally stated as H0 : m1 = m2 , where m1 is population mean of one population and m2 is population mean of the second population, assuming both the populations to be normal populations. Alternative hypothesis may be of not equal to or less than or greater than type as stated earlier and accordingly we shall determine the acceptance or rejection regions for testing the hypotheses. There may be different situations when we are examining the significance of difference between two means, but the following may be taken as the usual situations:

  1. Population variances are known or the samples happen to be large samples:
    In this situation we use z-test for difference in means and work out the test statistic z as under:test statistic z
  2. Samples happen to be large but presumed to have been drawn from the same population whose variance is known:
    In this situation we use z test for difference in means and work out the test statistic z as Under
    z test for difference in means
  3. Samples happen to be small samples and population variances not known but assumed to be equal:
    In this situation we use t-test for difference in means and work out the test statistic t as under:
    t-test for difference in means

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