Comparing the means of two independent population when the population variances are known and unknown
Suppose you conduct a study and intend to use a hypothesis test to compare the means of two independent populations. Your null hypothesis is that the two means are equal. That is, \(\mathrm{H}_{0}: \mu_{1}=\mu_{2}\), or equivalently, \(\mathrm{H}_{0}: \mu_{1}-\mu_{2}=0\). Following is a table of the information you gather. Assume the populations from which your samples are drawn are both normally distributed.
| Sample Size | Sample Mean | Sample Variance | |
|---|---|---|---|
| Sample 1 | n_(1)=41 | bar(x)_(1)=14.3 | s_(1)^(2)=67.24 |
| Sample 2 | n_(2)=21 | bar(x)_(2)=13.6 | s_(2)^(2)=46.24 |
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