題組內容

1.5. (10%) The data consists of n independently selected pairs
$(X_i, Y_i), i=1,2,\dots,n$. The variances of X and Y are $\sigma_x^2$ and $\sigma_y^2$, respectively.
Let $D_i = X_i - Y_i$, the $D_i$'s are assumed to be normally distributed with variance $\sigma_D^2$ and the correlation between $X_i$ and $Y_i$ is $\rho$.

b. If the two-sample t test is incorrectly used to analyze paired data, what will happen to the t value if $\rho > 0$ (underestimated or overestimated)? Justify your answer.