设(X1,X2,.,X8)是取自正态总体N(μ1,σ^2 )的一个样本,设(Y1,Y2 ,.,-|||-Y9)是取自正态总体N(μ2,σ^2)的一个样本,两个总体相互独立,且 overline (X)=dfrac (1)(8)sum _(i=1)^8X, ,overline (Y)=-|||-dfrac (1)(9)sum _(i=1)^9(Y)_(j), ({S)_(奇)}^2=dfrac (1)(15)[ sum _(i=1)^8(({X)_(i)-overline (X))}^2+sum _(i=1)^9(({Y)_(i)-overline (Y))}^2] ,证明: =dfrac (overline {X)-overline (Y)-((mu )_(1)-(mu )_(2))}({S)_(20)sqrt (dfrac {1)(8)+dfrac (1)(9)}}sim t(15) .