- Pooled Variances - Pooled Variances

Hypothesis Tests for \(\mu_1− \mu_2\): The Pooled t-test

Now let's consider the hypothesis test for the mean differences with pooled variances.




The assumptions/conditions are:

  • The populations are independent
  • The population variances are equal
  • Each population is either normal or the sample size is large

Test Statistic:

The test statistic is...


And \(t^*\) follows a t-distribution with degrees of freedom equal to \(df=n_1+n_2-2\).

The p-value, critical value, and conclusion are found similar to what we have done before.

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