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概率论题库 #10927提高
选择题假设检验提高

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#10927
设 X1,X2,⋯ ,Xn{X}_{1},{X}_{2},\cdots,{X}_{n} 为来自正态总体 N(μ,2)N\left({\mu,2}\right) 的简单随机样本,记 Xˉ=1n∑i=1nXi,zα\bar{X} = \frac{1}{n}\mathop{\sum }\limits_{i = 1}^{n}{X}_{i},{z}_{\alpha } 表示标准正态分布的上 α\alpha 分位数. 假设检验问题: H0:μ≤1,H1:μ>1{H}_{0}: \mu \leq 1,{H}_{1}: \mu > 1 的显著性水平为 α\alpha 的检验的拒绝域为‾\underline{\qquad}.

A. {(X1,X2,⋯ ,Xn)∣Xˉ≥1+2nzα}\left\{ {\left({{X}_{1},{X}_{2},\cdots,{X}_{n}}\right) \mid \bar{X} \geq 1 + \frac{2}{n}{z}_{\alpha }}\right\}
B. {(X1,X2,⋯ ,Xn)∣  Xˉ≥1+2nzα}\left\{ {\left({{X}_{1},{X}_{2},\cdots,{X}_{n}}\right) \mid \;\bar{X} \geq 1 + \frac{\sqrt{2}}{n}{z}_{\alpha }} \right\}
C. {(X1,X2,⋯ ,Xn)∣Xˉ≥1+2nzα}\left\{ {\left({{X}_{1},{X}_{2},\cdots,{X}_{n}}\right) \mid \bar{X} \geq 1 + \frac{2}{\sqrt{n}}{z}_{\alpha }}\right\}
D. {(X1,X2,⋯ ,Xn)∣  Xˉ≥1+2nzα}\left\{ {\left({{X}_{1},{X}_{2},\cdots,{X}_{n}}\right) \mid \;\bar{X} \geq 1 + \sqrt{\frac{2}{n}}{z}_{\alpha }} \right\}

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