Re: 請問一題統計問題
※ 引述《aspiren (對ptt又愛又恨..)》之銘言：
: 請幫我看看這題~
: Consider the following hypothesis test:
: Ho: p < =0.8 vs Ha: p > 0.8
: A sample of 400 provided a sample proportion of 0.853.
: (a) Using α=0.05, what is the conclusion based on hypothesis test?
: (b) Using α=0.001, what is the conclusion based on p-value?
: 感謝!!
r.v X ~ Ber(p)
iid
X1,X2,...,X400 ～ Ber(p)
^ X1+X2+...+X400 n≧30 p(1-p)
p = ---------------- ～ N(p, ------ )
400 by CLT 400
Ho: p≦0.8 vs Ha: p＞0.8
(a)
^
p - po
檢定統計量為 Z = -------------- 檢定規則：
1
--- Reject Ho at α=0.05 if Zo > Zα
2
po(1-po)
（----------）
400
∴ Zo = 2.65 > Zα=1.645 at α=0.05
Therefore, Reject Ho 有足夠證據顯示p>0.8
(b)
^ ^
* 0.853 - 0.8
P-value = P( p > p ) = P( Z > -------------- ) =0.004
0.02
∵0.004 > 0.001 ∴ Do not reject Ho
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