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