3 A photocopier in a school is known to break down at random at a mean rate of 8 times per week.
- Give a reason why a Poisson distribution could be used to model the number of breakdowns.
The headteacher of the school replaces the photocopier with a refurbished one and wants to find out if the rate of breakdowns has increased or decreased.
- Write down suitable null and alternative hypotheses that the headteacher should use.
The refurbished photocopier was monitored for the first week after it was installed.
- Using a \(5 \%\) level of significance, find the critical region to test whether the rate of breakdowns has now changed.
- Find the actual significance level of a test based on the critical region from part (c).
During the first week after it was installed there were 4 breakdowns.
- Comment on this finding in the light of the critical region found in part (c).