keywords: Harmonic mean of variances, chi-square distribution, directional alternative hypothesis
In this study, we proposed a test statistic for testing equality of means when variances are not equal. When variances of different groups are significantly different from one another it is not proper to use the pooled sample variance ( ) as a single value for the variances. In this work we are interested in testing directional hypothesis, since the variances are unequal then we make use of harmonic mean variance ( ). The means are ranked such that the problem reduces to a two sample situations. Data set from Kwara State Ministry of Agriculture on the yield of maize (kilograms) in four different locations was used to demonstrate directional hypothesis testing.
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