Pooled-deviation calculation with an incorrect result

Read the equation

The formula shown is the pooled standard deviation, but substituting the written values gives approximately 0.0424265, not 0.0300. The denominator 1998 correctly adds the two degrees of freedom; the final square root was evaluated incorrectly in the source. The recovered CSV audit, using unrounded values, gives about 0.0424158753.

Terms & definitions

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Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

• Preserve the original expression and display the corrected evaluation beside it.

Original context

\bar{x}_2 &= 0.9115, \quad s_2 = 0.0600, \quad n_2 = 1000
\end{align}

\begin{equation}
s_p = \sqrt{\frac{999 \cdot 0.0001^2 + 999 \cdot 0.0600^2}{1998}} = 0.0300
\end{equation}

\begin{equation}
d = \frac{0.9115 - 0.2499}{0.0300} = 22.06
\end{equation}

\textbf{t-statistic Calculation:}

s_p = \sqrt{\frac{999 \cdot 0.0001^2 + 999 \cdot 0.0600^2}{1998}} = 0.0300

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