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).

a. Find the sample correlation between instructor ratings and expected grades.1
b. Test, at the 10% significance level, the hypothesis that the population correlation coefficient is zero against the alternative that it is positive.

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Instructor 2.8 3.7 4.4 3.6 4.7 3.5 4.1 3.2 4.9 4.2 3.8 3.3 rating Expected 2.6 29 3.3 3.2 3.1 2.8 2.7 2.4 3.5 3.0 34 2.5 grade