[問題] 雲科財金考古題 求beta值

看板Statistics作者 (無)時間14年前 (2011/10/21 20:41), 編輯推噓1(1推 0噓 5→)
留言6則, 2人參與, 最新討論串1/1
題目如下 Let X1,X2,...,X19 be a random sample of size n=19 from the normal distribution N(u,sigma^2). Find the approximate value of Beta, the probability of type II error, For the critical region C.(Alpha=0.05, for testing H0: sigma^2=30, H1: sigma^2=80 不知要從哪裡下手，有人可以教我嗎?謝謝~!! -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.194.46.178
推
10/22 00:12, , 1F
Under H0 , Q = (19-1)S^2/30 ~ χ^2(19-1)
10/22 00:12, 1F
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10/22 00:14, , 2F
Reject H0 if Q>χ^2_0.05(18)=28.87 => S^2>48.12
10/22 00:14, 2F
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10/22 00:15, , 3F
Beta risk = P(Accept H0|H1) = P(S^2≦48.12|σ^2=80)
10/22 00:15, 3F
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10/22 00:16, , 4F
=P(χ^2(18)≦(19-1)*48.12/80)=P(χ^2(18)≦11.43)
10/22 00:16, 4F
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10/22 00:18, , 5F
=0.1248 如果沒計算錯就這樣吧
10/22 00:18, 5F
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10/23 21:47, , 6F
謝謝~!!
10/23 21:47, 6F
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