You wanted to determine whether the ear choice a cell phone user uses is associated with auditory or language brain hemispheric dominance. Assume that you want to test the claim that handedness and cell phone ear preference are independent of each other using a 0.005 significance level.

You observed students on campus using a cell phone, and, when their call was finished, asked them whether they were Right or Left handed. (In your data, "No Preference" corresponds to the student switching the phone from ear to ear throughout their call.)
\begin{tabular}{|c|l|l|l|}
\hline & Right Ear & Left Ear & No Preference \\
\hline \hline Right Handed & 41 & 13 & 39 \\
\hline Left Handed & 39 & 9 & 26 \\
\hline
\end{tabular}

The expected observations for this table would be
\begin{tabular}{|l|l|l|l|}
\hline & Right Ear & Left Ear & No Preference \\
\hline Right Handed & & & \\
\hline Left Handed & & & \\
\hline
\end{tabular}

The resulting Pearson residuals are:
\begin{tabular}{|l|l|l|l|}
\hline & Right Ear & Left Ear & No Preference \\
\hline Right Handed & & \\
\hline Left Handed & & & \\
\hline
\end{tabular}

What is the chi-square test-statistic for this data?
\[
\chi^{2}=
\]

Step 1 ：Calculate the row totals: Right Handed: \(41 + 13 + 39 = 93\), Left Handed: \(39 + 9 + 26 = 74\)

Step 2 ：Calculate the column totals: Right Ear: \(41 + 39 = 80\), Left Ear: \(13 + 9 = 22\), No Preference: \(39 + 26 = 65\)

Step 3 ：Calculate the grand total: \(93 + 74 = 167\)

Step 4 ：Calculate the expected frequencies: Right Handed, Right Ear: \(\frac{93 * 80}{167} = 44.43\), Right Handed, Left Ear: \(\frac{93 * 22}{167} = 12.28\), Right Handed, No Preference: \(\frac{93 * 65}{167} = 36.29\), Left Handed, Right Ear: \(\frac{74 * 80}{167} = 35.57\), Left Handed, Left Ear: \(\frac{74 * 22}{167} = 9.72\), Left Handed, No Preference: \(\frac{74 * 65}{167} = 28.71\)

Step 5 ：Calculate the Pearson residuals: Right Handed, Right Ear: \(\frac{41 - 44.43}{\sqrt{44.43}} = -0.52\), Right Handed, Left Ear: \(\frac{13 - 12.28}{\sqrt{12.28}} = 0.20\), Right Handed, No Preference: \(\frac{39 - 36.29}{\sqrt{36.29}} = 0.45\), Left Handed, Right Ear: \(\frac{39 - 35.57}{\sqrt{35.57}} = 0.58\), Left Handed, Left Ear: \(\frac{9 - 9.72}{\sqrt{9.72}} = -0.23\), Left Handed, No Preference: \(\frac{26 - 28.71}{\sqrt{28.71}} = -0.50\)

Step 6 ：Calculate the chi-square test statistic: \((-0.52)^2 + (0.20)^2 + (0.45)^2 + (0.58)^2 + (-0.23)^2 + (-0.50)^2 = 0.27 + 0.04 + 0.20 + 0.34 + 0.05 + 0.25 = 1.15\)

Step 7 ：\(\boxed{\text{The chi-square test statistic for this data is 1.15}}\)