2 A traffic officer notes the speeds of vehicles as they pass a certain point. In the past the mean of these speeds has been \(62.3 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) and the standard deviation has been \(10.4 \mathrm {~km} \mathrm {~h} ^ { - 1 }\). A speed limit is introduced, and following this, the mean of the speeds of 75 randomly chosen vehicles passing the point is found to be \(59.9 \mathrm {~km} \mathrm {~h} ^ { - 1 }\).

1. Making an assumption that should be stated, test at the \(2 \%\) significance level whether the mean speed has decreased since the introduction of the speed limit.
2. Explain whether it was necessary to use the Central Limit theorem in part (i).