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  • https://stats.libretexts.org/Workbench/Introduction_to_Statistical_Methods_(Yuba_College)/10%3A_Hypothesis_Tests_and_Confidence_Intervals_for_Two_Populations/10.05%3A_Chapter_10_Formulas
    &t=\frac{\left(\bar{x}_{1}-\bar{x}_{2}\right)-\left(\mu_{1}-\mu_{2}\right)}{\sqrt{\left(\frac{\left(n_{1}-1\right) s_{1}^{2}+\left(n_{2}-1\right) s_{2}^{2}}{\left(n_{1}+n_{2}-2\right)}\right)\left(\fr...&t=\frac{\left(\bar{x}_{1}-\bar{x}_{2}\right)-\left(\mu_{1}-\mu_{2}\right)}{\sqrt{\left(\frac{\left(n_{1}-1\right) s_{1}^{2}+\left(n_{2}-1\right) s_{2}^{2}}{\left(n_{1}+n_{2}-2\right)}\right)\left(\frac{1}{n_{1}}+\frac{1}{n_{2}}\right)}} \\ df=(s21n1+s22n2)2((s21n1)2(1n11)+(s22n2)2(1n21))
  • https://stats.libretexts.org/Workbench/Statistics_for_Behavioral_Science_Majors/08%3A_Hypothesis_Tests_and_Confidence_Intervals_for_Two_Populations/8.05%3A_Two_Population_Formulas
    &t=\frac{\left(\bar{x}_{1}-\bar{x}_{2}\right)-\left(\mu_{1}-\mu_{2}\right)}{\sqrt{\left(\frac{\left(n_{1}-1\right) s_{1}^{2}+\left(n_{2}-1\right) s_{2}^{2}}{\left(n_{1}+n_{2}-2\right)}\right)\left(\fr...&t=\frac{\left(\bar{x}_{1}-\bar{x}_{2}\right)-\left(\mu_{1}-\mu_{2}\right)}{\sqrt{\left(\frac{\left(n_{1}-1\right) s_{1}^{2}+\left(n_{2}-1\right) s_{2}^{2}}{\left(n_{1}+n_{2}-2\right)}\right)\left(\frac{1}{n_{1}}+\frac{1}{n_{2}}\right)}} \\ df=(s21n1+s22n2)2((s21n1)2(1n11)+(s22n2)2(1n21))

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