A lecture wanted to compare his teaching methods towards 2 different class. The first class, he took 10 students randomly while the second class he took 8 students randomly as well and note it as below:
| N1 | N2 | N3 | N4 | N5 | N6 | N7 | N8 | N9 | N10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Class 1 | 77 | 74 | 49 | 68 | 86 | 80 | 71 | 77 | 81 | 72 |
| Class 2 | 78 | 57 | 65 | 82 | 73 | 76 | 54 | 56 | - | - |
Hypothesis
$$ H_0 : \mu1 = \mu2
$$
$$ H_1 : \mu \neq \mu2 $$
Formula
$$ t = \frac{\bar{x_1}-\bar{x_2}}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} $$
$$ DF=n_1 +n_2-2 $$
$$ S_p=\sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}} $$