A teacher is wondering if 1st period students tend to do better on tests than 2nd period students. She takes a random sample of 5 1st period students whose scores were 98, 86, 75, 92, and 90. She takes a random sample of 3 2nd period students whose scores were 91, 89, and 87. Suppose that the original distributions of scores are normally distributed. Do these data give evidence that the 1st period students do better?

Perform the appropriate hypothesis test. Show all work.