4. Rugby players sometimes use protein powder to aid muscle increase. The monthly weight gains of rugby players taking protein powder may be modelled by a normal distribution having a standard deviation of 40 g and a mean which may depend on the type of protein powder they consume. A rugby team coach gives the same amount of protein powder over a trial month to 22 randomly selected players. Protein powder \(A\) was used by 12 players, randomly selected, and their mean weight gain was 900 g . Protein powder \(B\) was used by the other 10 players and their mean weight gain was 870 g . Let \(\mu _ { A }\) and \(\mu _ { B }\) be the mean monthly weight gains, in grams, of the populations of rugby players who use protein powder \(A\) and protein powder \(B\) respectively.

1. Calculate a 98\% confidence interval for \(\mu _ { A } - \mu _ { B }\).
2. In the given context, what can you conclude from your answer to part (a)? Give a reason for your answer.
3. Find the confidence level of the largest confidence interval that would lead the coach to favour protein powder \(A\) over protein powder \(B\).
4. State one non-statistical assumption you have made in order to reach these conclusions.