## Statistics (12th Edition)

To find the test statistic, we need pooled standard deviation. $s_{p} = \sqrt \frac{{(n_{1}-1)s_{1}^{2} + (n_{2}-1)s_{2}^{2}}}{n_{1} + n_{2} - 2}$ $=\sqrt \frac{(20 - 1)(1.98)^{2} + (20 - 1)(2.13)^{2}}{20 + 20 - 2}$ $= \sqrt {\frac{74.4876 + 86.2011}{38}}$ =2.0564 $t = \frac{x̅_{1} - x̅_{2}}{s_{p} \sqrt {1/n_{1} + 1/n_{2}}}$ $= \frac{3.70 - 3.30}{2.0564 \sqrt {1/20 + 1/20}}$ = 0.6151