5.6.1.1 - Pooled Variances
5.6.1.1 - Pooled VariancesHypothesis Tests for \(\mu_1− \mu_2\): The Pooled t-test
Now let's consider the hypothesis test for the mean differences with pooled variances.
Null:
\(H_0\colon\mu_1-\mu_2=0\)
Conditions:
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...
\(t^*=\dfrac{\bar{x}_1-\bar{x}_2-0}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\)
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.