5 In a particular town, a survey was conducted on a sample of 200 residents aged 41 years to 50 years. The survey questioned these residents to discover the age at which they had left full-time education and the greatest rate of income tax that they were paying at the time of the survey.
The summarised data obtained from the survey are shown in the table.
| \multirow{2}{*}{Greatest rate of income tax paid} | Age when leaving education (years) | \multirow[b]{2}{*}{Total} |
| 16 or less | 17 or 18 | 19 or more | |
| Zero | 32 | 3 | 4 | 39 |
| Basic | 102 | 12 | 17 | 131 |
| Higher | 17 | 5 | 8 | 30 |
| Total | 151 | 20 | 29 | 200 |
- Use a \(\chi ^ { 2 }\)-test, at the \(5 \%\) level of significance, to investigate whether there is an association between age when leaving education and greatest rate of income tax paid.
- It is believed that residents of this town who had left education at a later age were more likely to be paying the higher rate of income tax. Comment on this belief.
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