104關務 統計第三題 - 考試

By James
at 2015-04-18T17:24
at 2015-04-18T17:24
Table of Contents
題目說:自AB兩個國家進口水果,抽驗是否農藥殘留超標,
A國100件抽出67件超標,B國150件抽出93件超標,
政府想瞭解A國水果有農藥殘留超標的比例是否大於B國,顯著水準10%。
(一)設立假說
(二)以信賴區間法驗證假說
(三)以p值法驗證
有兩個地方想請問,
1. 第二題的信賴區間跟第三題p-value用的標準差是不是不同?
我記得上課時老師說過,做P1-P2的信賴區間估計,
標準差要用√(p1q1/n1+p2q2/n2)。
但是做統計檢定的時候,除非H0有告訴你P1-P2可能為多少,不然
標準差要用√(1/n1+1/n2)*(p_hat)*(1-p_hat)
其中p_hat = (x1+x2)/(n1+n2)
但是用信賴區間法檢定,我就不確定要不要把H0的假設放進標準差的估計了。
我考試時我是統一用後者,請有做過這類題目的版友解惑。
2.這題是考單尾信賴區間,我想請問是求P1-P2的下限嗎?
考試時衝太快,當成雙尾在算,回家後仔細想想,
我是把信賴區間用統計檢定去反推,推出來的是下限,
∵ Pr(Z < Zα) = 1-α (因為要做1-α的信賴區間)
[(P1_hat-P2_hat) - (P1-P2)]/sd(P1_hat-P2_hat) < Zα
P1-P2 > (P1_hat-P2_hat) - Zα*sd(P1_hat-P2_hat)
故 P1-P2的1-α信賴區間為[(P1_hat-P2_hat) - Zα*sd(P1_hat-P2_hat),∞]
看下限算出來是否大於0,如果大於0則拒絕H0。
想請教我的想法對嗎?
文長且參雜大量數學符號,謝謝看完。
--
A國100件抽出67件超標,B國150件抽出93件超標,
政府想瞭解A國水果有農藥殘留超標的比例是否大於B國,顯著水準10%。
(一)設立假說
(二)以信賴區間法驗證假說
(三)以p值法驗證
有兩個地方想請問,
1. 第二題的信賴區間跟第三題p-value用的標準差是不是不同?
我記得上課時老師說過,做P1-P2的信賴區間估計,
標準差要用√(p1q1/n1+p2q2/n2)。
但是做統計檢定的時候,除非H0有告訴你P1-P2可能為多少,不然
標準差要用√(1/n1+1/n2)*(p_hat)*(1-p_hat)
其中p_hat = (x1+x2)/(n1+n2)
但是用信賴區間法檢定,我就不確定要不要把H0的假設放進標準差的估計了。
我考試時我是統一用後者,請有做過這類題目的版友解惑。
2.這題是考單尾信賴區間,我想請問是求P1-P2的下限嗎?
考試時衝太快,當成雙尾在算,回家後仔細想想,
我是把信賴區間用統計檢定去反推,推出來的是下限,
∵ Pr(Z < Zα) = 1-α (因為要做1-α的信賴區間)
[(P1_hat-P2_hat) - (P1-P2)]/sd(P1_hat-P2_hat) < Zα
P1-P2 > (P1_hat-P2_hat) - Zα*sd(P1_hat-P2_hat)
故 P1-P2的1-α信賴區間為[(P1_hat-P2_hat) - Zα*sd(P1_hat-P2_hat),∞]
看下限算出來是否大於0,如果大於0則拒絕H0。
想請教我的想法對嗎?
文長且參雜大量數學符號,謝謝看完。
--
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