4 A researcher is investigating the sizes of pebbles at various locations in a river. Three sites in the river are chosen and each pebble sampled at each site is classified as large, medium or small. The results are as follows.
| Site | \multirow{2}{*}{} |
| \cline { 3 - 6 }
\multicolumn{2}{|c|}{} | A | B | C | |
| \multirow{3}{*}{} | Large | 15 | 12 | 10 | 37 |
| \cline { 2 - 6 } | Medium | 28 | 17 | 45 | 90 |
| \cline { 2 - 6 } | Small | 47 | 33 | 36 | 116 |
| Column totals | 90 | 62 | 91 | 243 |
- Carry out a test at the \(5 \%\) significance level to examine whether there is any association between pebble size and site. Your working should include a table of the contributions of each cell to the test statistic.
- By referring to each site, comment briefly on how the size of the pebbles compares with what would be expected if there were no association. You should support your answers by referring to your table of contributions.