The type of distribution to use for the test statistics and state the level of significance.

A professor is concerned that the two sections of college algebra that he teaches are not performing at the same level. To test his claim, he looks at the mean exam score for a random sample of students from each of his classes. In Class1, the mean exam for 12 students is 78.7 with a standard deviation of 6.5. In Class 2, the mean exam core for 15 students is 81.1 with a standard deviation of 7.4. Assume that the population variances are equal.
Given that the difference between two populations means when both population variances are unknown but assumed to be equal and random samples drawn are independent. Both the population distributions are approximately normal. The t-test statistic for equal variances is appropriate. The level of significance for this test is $\alpha =0.05$.
Therefore, the t-test statistic for equal variances is appropriate and the level of significance for this test is $\alpha =0.05$.