Let two independent random samples of sizes n_1 and n_2 respectively have been drawn from the same normal population. Let X_1 and X_2 be the means…

Options

1. A

   $t = \frac{\overline{X_1} - \overline{X_2}}{S / \sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$t=S/n1​1​−n2​1​​X1​​−X2​​​ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$S=n1​+n2​−2n1​s12​+n2​s22​​​

2. B

   $t = \frac{\overline{X_1} - \overline{X_2}}{s /\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$t=s/n1​1​+n2​1​​X1​​−X2​​​ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$S=n1​+n2​−2n1​s12​+n2​s22​​​

3. C

   $t = \frac{\overline{X_1} - \overline{X_2}}{S \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$t=Sn1​1​+n2​1​​X1​​−X2​​​ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$S=n1​+n2​−2n1​s12​+n2​s22​​​

4. D

   $t = \frac{\overline{X_1} + \overline{X_2}}{s \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$t=sn1​1​+n2​1​​X1​​+X2​​​ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$S=n1​+n2​−2n1​s12​+n2​s22​​​

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