7. Branwen intends to buy a new bike, either a Cannotrek or a Bianchondale. If there is evidence that the difference in the mean times on the two bikes over a 10 km time trial is more than 1.25 minutes, she will buy the faster bike. Otherwise, she will base her decision on other factors. She negotiates a test period to try both bikes. The times, in minutes, taken by Branwen to complete a 10 km time trial on the Cannotrek may be modelled by a normal distribution with mean \(\mu _ { C }\) and standard deviation \(0 \cdot 75\). The times, in minutes, taken by Branwen to complete a 10 km time trial on the Bianchondale may be modelled by a normal distribution with mean \(\mu _ { B }\) and standard deviation \(0 \cdot 6\). During the test period, she completes 6 time trials with a mean time of 19.5 minutes on the Cannotrek, and 5 time trials with a mean time of 17.3 minutes on the Bianchondale. She calculates a \(p \%\) confidence interval for \(\mu _ { C } - \mu _ { B }\).

1. What would be the largest value of \(p\) that would lead Branwen to base her purchasing decision on the time trials, without considering other factors?
2. State an assumption you have made in part (a).