Re: [課業] 102關務抽樣 計算題參考答案
第一題
資料:N1/N=0.7, N2/N=0.3 , n=100, n1/n=0.4 ,n2/n=0.6 ,p1=4/40 ,p2=12/60
(1).簡單抽樣法
p=(4+12)/100=0.16 var=(0.16*0.84*(100/99))/100=0.001357575
(2).事後分層法
1.所謂事後分層法,是用來改進事前分層法或未回覆資料所造成的誤差,
傳統的分層法是假設母體比重已知..但事實上在做調查時不太可能的,
只能"假設"母體比例,在做完調查(普查)時發現母體比例和之前假設有
很大的差距,就必須改用事後分層法
2.使用時機:
以這題為例W1=0.7...W2=0.3....和w1=0.4..w2=0.6..有所差距而且每一層
抽的樣本不會太少,因此要改用事後分層..
3.計算:
p=0.7*(4/40)+0.3*(12/60)=0.13
var=(0.7*0.1*0.9*(40/39)+0.3*0.2*0.8*60/59)/100
+(0.3*0.1*0.9*40/39+0.7*0.2*0.8*60/59)/10000= 0.00114844806
(3)比較:
因事後分層的VAR較小..因此這題應改採用事後分層法
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