如何计算置信区间

Question

如题所述

Answer 1

(1)
若已知σ=0.01，统计量Y=(X拔-u)/σ ~ N(0,1)
当P(-c<=Y<=c)=0.9，查表得：c=1.65
则-c<=(X拔-u)/σ<=c
X拔-cσ<=u<=X拔+cσ 是u的0.90置信区间
计算得知为[2.1085,2.1415]
(2)
若未知σ，统计量T=√n*(X拔-u)/S ~ t(15)
S^2=1/n-1*∑(xi-x拔)^2
当P(-c<=T<=c)=0.9，查表得：c=1.753
则-c<=√n*(X拔-u)/S <=c
X拔-cS/√n<=u<=X拔+cS/√n 是u的0.90置信区间
计算得知为[2.1175,2.1325]