Two Means - Unknown, Unequal Variance: Videos & Practice Problems

A school administrator wants to test whether the average test scores of students from two different districts are the same. Independent random samples are taken, and the scores are assumed to be normally distributed with equal variances.
District 1: ${\bar{x}}_1=78.5$, $s_1^2=16$, $n_1=30$
District 2: ${\bar{x}}_2=74.3$, $s_2^2=14.44$, $n_2=28$
Significance level: $\alpha =0.01$
Test the claim that the population means are equal.