N2013 P2 Q9

A motoring magazine editor believes that the figures quoted by car manufacturers for distances travelled per litre of fuel are too high. He carries out a survey into this by asking for information from readers. For a certain model of car, \(8\) readers reply with the following data, measured in km per litre.

\[14.0\quad12.5\quad11.0\quad11.0\quad12.5\quad12.6\quad15.6\quad13.2\]

1. Calculate unbiased estimates of the population mean and variance.[2]

The manufacturer claims that this model of car will travel \(13.8\text{ km}\) per litre on average. It is given that the distances travelled per litre for cars of this model are normally distributed.

2. Stating a necessary assumption, carry out a \(t\)-test of the magazine editor's belief at the \(5\%\) significance level.[5]