11.61 A college administers a student evaluation questionnaire for all its courses. For a random sample of 12 courses, the accompanying table and the data file Student Evaluation show both the average student ratings of the instructor (on a scale of 1 to 5), and the average expected grades of the students (on a scale of A = 4 to F = 0).

Instructor rating 2.8 3.7 4.4 3.6 4.7 3.5 4.1 3.2 4.9 4.2 3.8 3.3 Expected grade 2.6 2.9 3.3 3.2 3.1 2.8 2.7 2.4 3.5 3.0 3.4 2.5

a. Find the sample correlation between instructor ratings and expected grades.

b. Test, at the 10% significance level, the hypothesis that the population correlation coefficient is zero against the alternative that it is positive.