It is assumed that standardized test scores should be correlated with students classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizzes, etc.) would also perform well on a standardized test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she collects the following data for her (small) class:

Standardized test score      Overall GPA
              59                             2.1
              62                             2.0
              84                             3.2
              94                             3.2
              98                             3.6

(a) Estimate the expected GPA of a student who scored a 75 on the standardized test.
(b) Determine a 99% confidence interval for the expected value of a student who scored a 70 on the
standardized test.