Question2Allthefarmsinadistrictarestratifiedintoseven(7)strataaccordingtofarmsize.Thetotalnumberoffarms,themeannumberofhectaresofwheatperfarmineachstratumandthestandarddeviationforeachstratumaregiveninthetablebelow._________________________________________________________________________StratumFarmsizeNo.ofMeanwheatStandard(hectares)farms(hectares)deviation_____________________________________________________________10–203682.72.1221–404258.13.6341–6038912.13.9461–8031616.95.1581–10017420.86.16101–1209825.26.57121-13831.89.1____________________________________________________________________Question2(contd.)i)Ifwewanttosample100farms(ie,n=100)fromthepopulationaboveusingstratifiedrandomsampling,computestratumsamplesizesaccordingtoeachofthefollowingtwomethodsofallocation,separately:(a)proportionalallocation;(b)Neymanallocation.Answer：N=368+425+389+316+174+98+138=1908按比例分配时，各层的样本量为：19、22、20、17、9、5、7(b)=8385.7按尼曼分配时，各层应分配的样本为：9、18、18、19、13、8、15ii)Comparetheprecisionsofthesetwoallocationmethodsforestimatingmeannumberofhectaresofwheat(ie,varianceoftheestimatedmean),andcomment.Answer：proportionalallocation;Neymanallocation：因为，所以Neymanallocation更加精确。iii)Supposethatastratifiedsampleofsize100hasbeenobtainedaccordingtothestratumsamplesizesdeterminedbytheNeymanallocationinparti(b),withasamplemeanof2.5,7.5,13.5,16.0,21.5,23.0and32.5hectaresofwheatforeachstratumsample,respectively.Estimatethemeannumberofhectaresofwheatperfarm,andthecorresponding95%confidenceinterval.Answer：=(368/1908)×2.5+(425/1908)×7.5+(389/1908)×13.5+(316/1908)×16.0+(174/1908)×21.5+(98/1908)×23.0+(138/1908)×32.5=13.04769392≈13.048thecorresponding95%confidenceinterval:;t=1.96经计算：平均每个农场公顷数95%的置信区间为（12.215，13.881）公顷。iv)Estimatethevarianceoftheestimatedmeannumberofhectaresofwheatperfarmifasimplerandomsampleofthesamesize,100,wasobtained,andcomparetheprecision(ie,variance)oftheestimatedmeanherewiththatwhenusingthestratifiedsamplebasedontheNeymanallo