The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a major in the College of Humanities and Social Sciences (HSS major) or has a major in the College of Business (Business major). The school randomly surveys 10 seniors who are HSS students and 10 seniors who are Business students and asks them to rate how satisfied they are at the school on a scale of 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. Here are the data:
HSS Major: 7 6 10 4 8 9 6 8 7 10
Business Major: 4 7 4 6 8 7 9 5 8 7
The HSS majors have a mean of 7.5 and a variance of 3.6, whereas the Business majors have a mean of 6.5 and a variance of 2.9. Are the differences found between the HSS majors and Business majors statistically significant?