In the past, the number of house sales completed per week by a building company has been modelled by a random variable which has the distribution $Po\left( {0.8} \right)$. Following a publicity campaign, the builders hope that the mean number of sales per week will increase. In order to test at the 5% significance level whether this is the case, the total number of sales during the first 3 weeks after the campaign is noted. It is assumed that a Poisson model is still appropriate.

a) Given that the total number of sales during the 3 weeks is 5, carry out the test.

b) During the following 3 weeks the same test is carried out again, using the same significance level. Find the probability of a Type I error.

c) Explain what is meant by a Type I error in this context.

d) State what further information would be required in order to find the probability of a Type II error.