Course Notes - Department of Mathematics and Statistics

drug is more effective than the standard because the probabilityof 30 or more successes is less than 0.05. This indicates that theobserved 30 (or more) is not likely to occur unless the new drughas a beneficial effect.Fred’s Rugby TeamIs there enough evidence to suggest Fred’s coaching techniques are causingmore injuries than normal?Can this be dealt with using the binomial distribution? Does it satisfythe 3 assumptions?1. Independence ? We will assume that if one player injures their legthis has no effect on other players injurying theirleg.2. Binary outcome ? We can define the outcome as binary. Leg Injured/LegUninjured3. Constant probability of success? We will assume that the probabilityof injury is the same for everyone.So this problem can be tackled using a binomial distribution with n =15 and π = 0.15. We wish to know what is the probability that 5 ormore players are injured given these conditions. Using RCmdr we findthis probability is 0.0617. Since this probability is greater than 5%, thisis NOT a rare event, therefore there is no evidence Fred’s techniquesare causing more leg injuries than normal.What times would Fred’s players need running to be in the top 10% ofplayers?We can solve all these problems fairly easily using a computer, but itdoes help to draw some pictures to get an idea of what is going on. Thereason we draw these pictures, is that when we get our solution fromthe calculator we can decide if it is reasonable.86