Introduction
In this lesson, we'll continue our investigation of hypothesis testing. In this case, we'll focus our attention on a hypothesis test for the difference in two population
means μ1−μ2 for
two situations:
- a hypothesis test
based on the t-distribution, known as the pooled two-sample t-test, for μ1−μ2 when
the (unknown) population variances σ2X and σ2Y are
equal - a hypothesis test based on the t-distribution, known as Welch's t-test,
for μ1−μ2 when
the (unknown) population variances σ2X and Y are
not equal
Of course, because population variances are generally not known, there is no way of being 100% sure that the population variances are equal or not equal. In order
to be able to determine, therefore, which of the two hypothesis tests we should use, we'll need to make some assumptions about the equality of the variances based on our previous knowledge of the populations we're studying.