8 A new light was installed on a certain footpath. A town councillor decided to use a hypothesis test to investigate whether the number of people using the path in the evening had increased. Before the light was installed, the mean number of people using the path during any 20 -minute period during the evening was 1.01. After the light was installed, the total number, \(n\), of people using the path during 3 randomly chosen 20 -minute periods during the evening was noted.

1. Given that the value of \(n\) was 6 , use a Poisson distribution to carry out the test at the \(5 \%\) significance level.
2. Later a similar test, at the \(5 \%\) significance level, was carried out using another 3 randomly chosen 20 -minute periods during the evening. Find the probability of a Type I error.
3. State what is meant by a Type I error in this context.
4. State, in context, what further information would be needed in order to find the probability of a Type II error. Do not carry out any further calculation.
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