5. Charlie carried out a survey on the main type of investment people have.
The contingency table below shows the results of a survey of a random sample of people.
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | Main type of investment |
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | Bonds | Cash | Stocks |
| \multirow{2}{*}{Age} | \(25 - 44\) | \(a\) | \(b - e\) | \(e\) |
| \cline { 2 - 5 } | \(45 - 75\) | \(c\) | \(d - 59\) | 59 |
- Find an expression, in terms of \(a , b , c\) and \(d\), for the difference between the observed and the expected value \(( O - E )\) for the group whose main type of investment is Bonds and are aged \(45 - 75\)
Express your answer as a single fraction in its simplest form.
Given that \(\sum \frac { ( O - E ) ^ { 2 } } { E } = 9.62\) for this information, - test, at the \(5 \%\) level of significance, whether or not there is evidence of an association between the age of a person and the main type of investment they have. You should state your hypotheses, critical value and conclusion clearly. You may assume that no cells need to be combined.
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