AIR MATH

Math Question

You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.
\begin{tabular}{|l||l||l||}
\hline Category & Population #1 & Population #2 \\
\hline \hline A & 10 & 59 \\
\hline \hline B & 47 & 121 \\
\hline
\end{tabular}
The expected observations for this table would be
\begin{tabular}{|l|l|l|}
\hline \multicolumn{1}{|l|}{ Category } & Population \( \# 1 \) & Population \( \# 2 \) \\
\hline \hline A & \( \square \) & \( \square \) \\
\hline B & \( \square \) \\
\hline
\end{tabular}
The resulting Pearson residuals are:
\begin{tabular}{|l||l|l|}
\hline Category & Population #1 & Population #2 \\
\hline \hline A & B \\
\hline B & - \\
\hline
\end{tabular}
What is the chi-square test-statistic for this data?
\[
\chi^{2}=
\]

Solution

solution

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