2 A new running track has been developed and part of the testing procedure involves 7 randomly chosen athletes. They each run 100 m on both the old and new tracks.
The results are as follows.
| Athlete | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Time on old track \(( s )\) | 12.2 | 10.3 | 11.5 | 13.0 | 11.8 | 11.7 | 11.9 |
| Time on new track \(( s )\) | 11.1 | 10.5 | 11.0 | 12.6 | 11.0 | 10.9 | 12.0 |
The population mean times on the old and new tracks are denoted by \(\mu _ { \mathrm { O } }\) seconds and \(\mu _ { \mathrm { N } }\) seconds respectively. Stating any necessary assumption, carry out a suitable \(t\)-test of the null hypothesis \(\mu _ { \mathrm { O } } - \mu _ { \mathrm { N } } = 0\) against the alternative hypothesis \(\mu _ { \mathrm { O } } - \mu _ { \mathrm { N } } > 0\). Use a \(2 \frac { 1 } { 2 } \%\) significance level .