- A doctor believes that the diet of her patients and their health are not independent.
She takes a random sample of 200 patients and records whether they are in good health or poor health and whether they have a good diet or a poor diet. The results are summarised in the table below.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | Good health | Poor health |
| Good diet | 86 | 8 |
| Poor diet | 91 | 15 |
Stating your hypotheses clearly, test the doctor's belief using a \(5 \%\) level of significance. Show your working for your test statistic and state your critical value clearly.