7 The number of cars caught speeding on a certain length of motorway is 7.2 per day, on average. Speed cameras are introduced and the results shown in the following table are those from a random selection of 40 days after this.

1. Calculate unbiased estimates of the population mean and variance of the number of cars per day caught speeding after the speed cameras were introduced.
2. Taking the null hypothesis \(\mathrm { H } _ { 0 }\) to be \(\mu = 7.2\), test at the \(5 \%\) level whether there is evidence that the introduction of speed cameras has resulted in a reduction in the number of cars caught speeding.
3. State what is meant by a Type I error in words relating to the context of the test in part (ii). Without further calculation, illustrate on a suitable diagram the region representing the probability of this Type I error.