概率习题：统计量与抽样分布章节设总体X~N(μ,σ^2),已知样本容量n=24,样本方差s^2=12.5227,求总体标准差σ大于3的概率.
问题描述：
概率习题：统计量与抽样分布章节
设总体X~N(μ,σ^2),已知样本容量n=24,样本方差s^2=12.5227,求总体标准差σ大于3的概率.
答
Because (n-1)s^2/σ^2 ~ X^2(n-1), where X^2(n-1) is chi-squre distribution with n-1 degree of freedom. Let X^2(n-1) = (n-1)s^2/σ^2 => X^2(23) = 288.0221/σ^2 => if σ>3 then X^2(23)3) = p(X^2(23)