12 During the 2006 Christmas holiday, John, a maths teacher, realised that he had fallen ill during 65\% of the Christmas holidays since he had started teaching.
In January 2007, he increased his weekly exercise to try to improve his health.
For the next 7 years, he only fell ill during 2 Christmas holidays.
12
- Using a binomial distribution, investigate, at the \(5 \%\) level of significance, whether there is evidence that John's rate of illness during the Christmas holidays had decreased since increasing his weekly exercise.
[0pt]
[6 marks]
12 - State two assumptions, regarding illness during the Christmas holidays, that are necessary for the distribution you have used in part (a) to be valid.
For each assumption, comment, in context, on whether it is likely to be correct.
[0pt]
[4 marks]