A statistics instructor is concerned that after her students perform well on the first of two major examinations in the introductory-level class, their performance appears to drop off on the second. Since this pattern appears to repeat itself across many sections of the same statistics class at her university, she wants to confirm that the downward trend in performance on the two 100-point examinations is real. To this end, she collects the examination results from a random sample of n = 12 students from the previous academic year. The scores on Exam 1 are: 81, 89, 83, 81, 77, 82, 79, 88, 80, 81, 79, and 91. On Exam 2, they are: 78, 77, 69, 81, 78, 74, 76, 79, 83, 76, 79,and 74.

1. 1. Create an R data frame to organize this data into two variables and twelve observations.
   2. Calculate the point estimate of the difference between the two population means.