Two Independent Samples of Sizes 15 and 17 Are Randomly $\left( \mu _ { 1 } - \mu _ { 2 } \right) ?$

Two independent samples of sizes 15 and 17 are randomly selected from two normal populations with equal variances. Which of the following distributions should be used for developing confidence intervals and for testing hypotheses about the difference between the two population means $\left( \mu _ { 1 } - \mu _ { 2 } \right) ?$

A) The standard normal distribution
B) The t distribution with 32 degrees of freedom
C) The t distribution with 31 degrees of freedom
D) The t distribution with 30 degrees of freedom
E) Any continuous distribution since the sum of the two sample sizes exceeds 30