2.I.10H

A study of 60 men and 90 women classified each individual according to eye colour to produce the figures below.

\begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Blue & Brown & Green \ \hline Men & 20 & 20 & 20 \ \hline Women & 20 & 50 & 20 \ \hline \end{tabular}

Explain how you would analyse these results. You should indicate carefully any underlying assumptions that you are making.

A further study took 150 individuals and classified them both by eye colour and by whether they were left or right handed to produce the following table.

\begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Blue & Brown & Green \ \hline Left Handed & 20 & 20 & 20 \ \hline Right Handed & 20 & 50 & 20 \ \hline \end{tabular}

How would your analysis change? You should again set out your underlying assumptions carefully.

[You may wish to note the following percentiles of the $\chi^{2}$ distribution.

$\left.\begin{array}{ccccccc} & \chi_{1}^{2} & \chi_{2}^{2} & \chi_{3}^{2} & \chi_{4}^{2} & \chi_{5}^{2} & \chi_{6}^{2} \\ 95 \% \text { percentile } & 3.84 & 5.99 & 7.81 & 9.49 & 11.07 & 12.59 \\ 99 \% \text { percentile } & 6.64 & 9.21 & 11.34 & 13.28 & 15.09 & 16.81\end{array}\right]$

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