If the populations are normally distributed but the population variances are unknown the t-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

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Quizplus · Accepted Answer

When the populations are normally distributed but the population variances are unknown, the t-statistic, which accounts for the uncertainty in estimating the population standard deviation from the sample, can indeed be used for making inferences about the difference between two population means using two independent random samples. This approach is commonly applied in the independent samples t-test.

If the Populations Are Normally Distributed but the Population Variances