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? \[ \chi^{2}= \]

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