作者SONGya168 (整天念英文的日子)
看板Statistics
标题Re: 请问一题统计问题
时间Thu Nov 13 00:05:07 2008
※ 引述《aspiren (对ptt又爱又恨..)》之铭言：
: 请帮我看看这题~
: 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?
: 感谢!!
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
检定统计量为 Z = -------------- 检定规则：
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 有足够证据显示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
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 61.216.14.135