※ 引述《[email protected]》之铭言： > suppose the random variable X is normally distributed with meanμx and > variance 400,A random sample with 36 observations is drawn to test whether > of X is 100.Please answer the following questions. > 1.Suppose the statistical inference rule is set to reject the null hypothesis > whether the sample mean is greater then 106 or less then 94.What is the > probability of type I error committed with the inference rule? Test rule: Reject H0 if and only if Xbar>106 or Xbar<94 即 Not reject H0 iff. Xbar≦106 and Xbar≧94 Tyep 1 error: reject H0 while H0 is true. Type II error: not reject H0 while H0 is false. The null hypothesis (H0) is whether the mean μ of X is 100. (μX 省略 X) H0 is true <==> μ = 100. 故计算 the probability of type I error 当然在 μ=100 时计算. 而要计算机率的 event 是 "reject H0", 也就是 Xbar>106 or Xbar<94. > (a)0.929 (b)0.072 (c)0.833 (d)0.167 (e)None of the above > 2.following questions 1,What is the probability of type II error committed > with the inference rule when the true mean is 99? Tyep II error 指 H0 不成立时却 not reject H0, 即 μ≠100 但不 rehect H0. 因此, 计算 the probability of type II error 当然是 在 μ≠100 时. 而要计算机率的事件是 "not reject H0", 也就是 "94≦Xbar≦106". 但 μ≠100 有无限多个值,计 算机率必须取特定的值. 题目已明言 "when the true mean is 99" 当然是在 μ=99 时计算上述事件的机率. > 第一题用误差等於 Xbar正负Z(α/2)xσ√n 算α=0.072 > 但是第二题我就不知道怎麽算β -- 嗨!  你好! 祝事事如意, 天天 happy! 统计专业版, 需要你的支持! :) 无名小站 telnet://wretch.twbbs.org Statistics (统计方法讨论区) 盈月与繁星 telnet://ms.twbbs.org Statistics (统计：让数字说话) 成大计中站 telnet://bbs.ncku.edu.tw Statistics (统计方法及学理讨论区) 交大资讯次世代 telnet://bs2.twbbs.org Statistics (统计与机率) ★本文未经本人同意请勿转载; 回覆请勿全文引用, 请仅留下直接涉及部分。 -- 夫兵者不祥之器物或恶之故有道者不处君子居则贵左用兵则贵右兵者不祥之器非君子 之器不得已而用之恬淡为上胜而不美而美之者是乐杀人夫乐杀人者则不可得志於天下 矣吉事尚左凶事尚右偏将军居左上将军居右言以丧礼处之杀人之众以哀悲泣之战胜以 丧礼处之道常无名朴虽小天下莫能臣侯王若能守之万物将自宾天地相合以降甘露民莫 之令而自均始制有名名亦既有夫亦将知止知止可以不殆譬道之在天 163.15.188.87海