Statistics Graduate Level Quiz
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Two independent normal samples satisfy Xi∼N(μX,σ2)X_i\sim N(\mu_X,\sigma^2) for i=1,…,8i=1,\ldots,8 and Yj∼N(μY,4σ2)Y_j\sim N(\mu_Y,4\sigma^2) for j=1,…,10j=1,\ldots,10. Define Sp2=∑i=18(Xi−Xˉ)2+14∑j=110(Yj−Yˉ)216S_p^2=\frac{\sum_{i=1}^8(X_i-\bar X)^2+\frac14\sum_{j=1}^{10}(Y_j-\bar Y)^2}{16}.
Under H0:μX−μY=δ0H_0:\mu_X-\mu_Y=\delta_0, which statistic has an exact standard tt distribution?
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