![]() ![]() Since it is observed that \(|t| = 2.886 > t_c = 2.22\), it is then concluded that the null hypothesis is rejected. The formula used for the independent samples t-test will depend upon whether or not the population variances are assumed to be equal. See reflected in the fact that the formula used is different, and the degrees of freedom are different too. That is a rather technical topic, but in layman terms, if the population variances are equal, then the best choice is to basically pool the available sample variances toīut if they are not equal, things get a bit more complicated, and some technical corrections are needed, which is what you That the optimal choice for the standard error depends on whether the population standard deviations are equal or not. Why do we need to test for the equality of population variances? This is because there is the need to find the standard error for the test, and it turns out
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