15.
A researcher at a large company thinks that there may be some relationship between the numbers of working days lost due to illness per year and the ages of the workers in the company. The researcher selects a random sample of 190 workers. The ages of the workers and numbers of days lost for a period of 1 year are summarised below.
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | Working days lost |
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | \(\mathbf { 0 }\) to 4 | 5 to 9 | 10 or more |
| \multirow{3}{*}{Age} | Under 35 | 31 | 27 | 4 |
| \cline { 2 - 5 } | 35 to 50 | 28 | 32 | 8 |
| \cline { 2 - 5 } | Over 50 | 16 | 28 | 16 |
- Carry out a test at the \(1 \%\) significance level to investigate whether the researcher's belief appears to be true. Your working should include a table showing the contributions of each cell to the test statistic.
- For the 'Over 50 ' age group, comment briefly on how the working days lost compare with what would be expected if there were no association.