A Survey Conducted in a Small Town Yielded the Results

question 19

Essay

A survey conducted in a small town yielded the results shown in the table. $\begin{array}{l|lc} &\text { Men }&\text { Women } \\\hline \text { Plan to vote } & 105 & 87 \\\hline \text { Do not plan to vote } & 312 & 246\end{array}$
i) Test the claim that the intention to vote in the next presidential election is independent of the gender of the pel 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?

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Definitions:

Total Variable Overhead Variance

The difference between the expected and actual costs of variable overheads in a manufacturing or production process.

Variable Overhead

Costs that vary with the level of production output, such as materials, utilities, and commissions, contrary to fixed overheads.

Total Direct Materials Cost Variance

The difference between the budgeted cost of direct materials and the actual cost incurred for the materials.

Direct Materials

Raw materials that are directly used in the manufacturing of a product and can be easily traced to it.