7 A newspaper reports that the average price of unleaded petrol in the UK is 110.2 p per litre.
The price, in pence, of a litre of unleaded petrol at a random sample of 15 petrol stations in Yorkshire is shown below together with some output from software used to analyse the data.
| 116.9 | 114.9 | 110.9 | 113.9 | 114.9 |
| 117.9 | 112.9 | 99.9 | 114.9 | 103.9 |
| 123.9 | 105.7 | 108.9 | 102.9 | 112.7 |
\begin{table}[h]
| \(| l |\) | Statistics |
| n | 15 |
| Mean | 111.6733 |
| \(\sigma\) | 6.1877 |
| s | 6.4048 |
| \(\Sigma \mathrm { x }\) | 1675.1 |
| \(\Sigma \mathrm { x } ^ { 2 }\) | 187638.31 |
| Min | 99.9 |
| Q 1 | 105.7 |
| Median | 112.9 |
| Q 3 | 114.9 |
| Max | 123.9 |
\captionsetup{labelformat=empty}
\caption{Fig. 7.1}
\end{table}
| \(n\) | 15 |
| \(p > 0.15\) |
| Null hypothesis | | The data can be modelled | | by a Normal distribution |
|
| Alternative hypothesis | | The data cannot be | | modelled by a Normal | | distribution |
|
- Select a suitable hypothesis test to investigate whether there is any evidence that the average price of unleaded petrol in Yorkshire is different from 110.2 p. Justify your choice of test.
- Conduct the hypothesis test at the \(5 \%\) level of significance.