A car manufacturer claims that, on a motorway, the mean number of miles per gallon for the Panther car is more than 70. To test this claim a car magazine measures the number of miles per gallon, $x$, of each of a random sample of 20 Panther cars and obtained the following statistics.

$$\bar{x} = 71.2 \quad s = 3.4$$

The number of miles per gallon may be assumed to be normally distributed.

\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly and using a 5\% level of significance, test the manufacturer's claim.
[5]
\end{enumerate}

The standard deviation of the number of miles per gallon for the Tiger car is 4.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{1}
\item Stating your hypotheses clearly, test, at the 5\% level of significance, whether or not there is evidence that the variance of the number of miles per gallon for the Panther car is different from that of the Tiger car.
[6]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S4  Q5 [11]}}