(a) The sample test statistic follows a t-distribution with degrees of freedom given by $df=\frac{(s_1^2/n_1+s_2^2/n_2)^2}{(s_1^2/n_1)^2/(n_1-1)+(s_2^2/n_2)^2/(n_2-1)}$, where $s_1$ and $s_2$ are the sample standard deviations, $n_1$ and $n_2$ are the sample sizes,
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