Two Independent Samples of Sizes 35 and 40 Are Randomly $\mu _ { 1 } - \mu _ { 2 }$

Two independent samples of sizes 35 and 40 are randomly selected from two normally distributed populations. Assume that the population variances are unknown but equal. In order to test the difference between the population means, $\mu _ { 1 } - \mu _ { 2 }$ , the sampling distribution of the sample mean difference, $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ , is: $\begin{array}{|l|l|}\hline A&\text {normally distributed. }\\\hline B&\text {\( t \)-distributed with 75 degrees of freedom. }\\\hline C&\text {\( t \)-distributed with 73 degrees of freedom. }\\\hline D&\text {\( F \)-distributed with 34 and 39 degrees of freedom. }\\\hline\end{array}$