Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded.
Using a 5\% level of significance, find the critical region for a two-tailed test of the null hypothesis that 'the mean rate at which the lift breaks down is 4 times per month'. The probability of rejection in each of the tails should be as close to \(2.5 \%\) as possible.
Over a randomly selected 1 month period the lift broke down 3 times.
Test, at the \(5 \%\) level of significance, whether Liftsforall's claim is correct. State your hypotheses clearly.
State the actual significance level of this test.
! The residents in the block of flats have a maintenance contract with Liftsforall. The residents pay Liftsforall \(\pounds 500\) for every quarter ( 3 months) in which there are at most 3 breakdowns. If there are 4 or more breakdowns in a quarter then the residents do not pay for that quarter.
Liftsforall installs a new lift in the block of flats.
Given that the new lift breaks down at a mean rate of 2 times per month,
find the probability that the residents do not pay more than \(\pounds 500\) to Liftsforall in the next year.