To see what difference class attendance made, a professor sampled grades from his large statistics class of 530 students. From the 220 students who attended class less than half the time (the "irregulars"), he took a random sample of 5 grades. From the remaining 310 students who attended at least half the time (the "regulars"), he took an independent random sample of 5 other grades:

Irregular Grades: 41, 81, 52, 62, 69

Regular Grades: 69, 56, 83, 70, 92

1. Construct a 95% confidence interval for the mean difference between the two groups of students?
2. To what extent does this support the contention that "it is worth 13 marks to come to class regularly?"