A Survey Conducted in a Small Town Yielded the Results

Essay

A survey conducted in a small town yielded the results shown in the table. $\begin{array}{l|lc} & \multicolumn{2}{|l}{\text { Men Women }} \\\hline \text { Plan to vote } & 105 & 87 \\\hline \text { Do not plan to vote } & 312 & 246\end{array}$

i) Test the claim that the intention to vote in the next presidential election is independent of the gender of the person being surveyed. Use a $0.05$ significance level.
ii) Using Yates' correction, replace $\sum \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ with $\sum \frac { ( | \mathrm { O } - \mathrm { E } | - 0.5 ) ^ { 2 } } { \mathrm { E } }$ and repeat the test. What effect does Yates' correction have on the value of the test statistic?