22.214.171.124 - Pooled Variances126.96.36.199 - 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
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.