Differences

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--- c:ma:2021:sample_questions [2021/10/07 01:13] – hkimscil
+++ c:ma:2021:sample_questions [2021/10/07 01:26] (current) – hkimscil
@@ Line 28: / Line 28: @@
 \end{eqnarray*}
+\begin{eqnarray*}
+se & = & \displaystyle s_{\overline{X_a}-\overline{X_b}} \\
+& = & \sqrt{\frac{S_p^2}{n_a} + \frac{S_p^2}{n_b}} \\
+& = & \sqrt{ \frac{40}{30} + \frac{40}{30} } \\
+& = & 1.632993
+\end{eqnarray*}
+\begin{eqnarray*}
+t_\text{calculated} & = & \displaystyle \frac{\text{difference}} {\text{random error}} \\
+& = & \displaystyle \frac{\text{difference}} {\text{standard error}} \\
+& = & \displaystyle \frac{30-20} {1.632993} \\
+& = & 6.123724
+\end{eqnarray*}
+<code>
+> 2320/58
+[1] 40
+> sqrt(8/3)
+[1] 1.632993
+> 10/sqrt(8/3)
+[1] 6.123724
+> qt(0.975, 58)
+[1] 2.001717
+>
+</code>
+\begin{eqnarray*}
+t_\text{critical}(\alpha=0.05, \text{df}=58) & = & 2.001717 \\
+\end{eqnarray*}