A small city is split into three neighbourhoods A, B, and C each of which has its own police station.

A small city is split into three neighbourhoods A, B, and C each of which has its own police station. The police chief wants how to allocate funds to each station and would like to test whether the crime rate varies between neighbourhoods. He believes the crime rate in each area is normally distributed. The three police station have recorded the number of crimes they dealt with for each of the last 25 years and this data has been summarised in the table below.

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Calculate a 95% confidence interval for the mean number of crimes in neighbourhood A and a 95% confidence interval for the mean number of crimes in B. Perform a hypothesis test at the 5% significance level for the null hypothesis that the variances of the crime rates for A and B are equal. Perform a test at the 5% significance level to to decide whether there is a difference between the mean crime rates in A and B. Justify any assumptions that you make in performing the test. Perform an analysis of variance to decide if the neighbourohood has an impact on the crime rate at a 1% level of significance. List the three assumptions underlying an analysis of variance test. Given a reason why one of them might not hold in this case.

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