Course Notes - Department of Mathematics and Statistics

ConclusionWhat conclusion would you draw about the proportion of lefthandedstudents in the different papers? We observed 70 left-handedstudents in the different paper. This is a rare event (the probabilityof 70 or more students being left-handed is less than 0.05). We canconclude that the proportion of left-handed students differs in the twopapers (i.e. π is greater than 11% in the different paper).FURTHER EXAMPLEIt is claimed cancer tumour size is halved in 30% of all patientsusing the current treatment. A new drug was used on 70 patientswith the cancer.(a) Suppose Y is the binomial random variable for the number ofpatients who have their tumour size halved. Write down the meanand standard deviation of Y . µ Y = nπ = 70 × 0.3 = 21 σ Y =√ √ nπ(1 − π) = 21 × 0.7 = 3.83(b) In a study, thirty out of seventy patients administered the standarddrug experience a halving of their tumours. Find the probabilitythat 30 or more out of 70 have their tumours halved. Pr(Y≥ 29.5)=pnorm(29.5,21,3.83,lower.tail=FALSE) = 0.0132(c) In a study 30 out of 70 patients in Auckland administered thisnew drug had their tumour size halved. What conclusion canbe drawn about the new drug? There is evidence that the new85