Assume thatprior to the construction it was established that the mean rate of accidents per month was 5.2and that the objective of the construction was to halve the accident rate. The situation can be represented by thefollowingtwo hypotheses:

H0: lambda=5.2(i.e.no change) vs H1: lambda=2.6as asserted by the engineers.

Note that we have simplified the continuous prior distribution for lambda used earlier in the question to a simple two-point discrete distribution.Now supposethat the probability that the nullhypothesis is true is 0.3.If there were a total of 22 accidents observed in 6 months, the posterior probability that the accident rate has halved is