two_sample_t-test
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| two_sample_t-test [2026/03/24 23:34] – [Two sample t-test] hkimscil | two_sample_t-test [2026/03/24 23:38] (current) – [Theory] hkimscil | ||
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| * p1의 샘플링분포 (distribution of sample means) | * p1의 샘플링분포 (distribution of sample means) | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| + | & & \text {Assuming that X1 and X2 are independent } \\ | ||
| \overline{X_{1}} & \sim & \left( \mu_{1}, \frac{\sigma_{1}}{n_{1}} \right) \\ | \overline{X_{1}} & \sim & \left( \mu_{1}, \frac{\sigma_{1}}{n_{1}} \right) \\ | ||
| \overline{X_{2}} & \sim & \left( \mu_{2}, \frac{\sigma_{2}}{n_{2}} \right) \\ | \overline{X_{2}} & \sim & \left( \mu_{2}, \frac{\sigma_{2}}{n_{2}} \right) \\ | ||
| & & \text{note that } n_{1}, n_{2} \text{ are sample size.} \\ | & & \text{note that } n_{1}, n_{2} \text{ are sample size.} \\ | ||
| + | & & \text{and } \frac{\sigma_{1}}{n_{1}} = Var \left[ \overline{X_{1}} \right] | ||
| \\ | \\ | ||
| Var \left[ \overline{X_{1}} - \overline{X_{2}} \right] & = & | Var \left[ \overline{X_{1}} - \overline{X_{2}} \right] & = & | ||
two_sample_t-test.txt · Last modified: by hkimscil