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magine that a professor of sociology has two teaching assistants (TAs) who will help him grade assignments for the duration of the semester. The professor wants to make sure that he and the TAs are well calibrated with one another, so he has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, he first converts the students’ scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in his class for each grader.   Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 1.43 1.05 0.39 Student 2 -0.57 -1.33 0.87 Student 3 0.35 0.27 -0.94 Student 4 0.72 0.90 2.24 Student 5 -1.41 -1.23 -0.50 Student 6 0.10 0.27 0.56 Student 7 -2.04 -1.71 -0.94 Student 8 0.76 1.19 0.03 Student 9 0.47 0.56 -0.50 Student 10 0.18 0.03 -1.21   The professor is going to use the z-scores to calculate the correlation coefficient between his scores and those of his TAs. To calculate the correlation coefficient, he sums the products of the z-scores. The professor should divide this sum by     .

- October 5, 2022 - Edwin Tunner
magine that a professor of sociology has two teaching assistants (TAs) who will help him grade assignments for the duration of the semester. The professor wants to make sure that he and the TAs are well calibrated with one another, so he has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, he first converts the students’ scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in his class for each grader.
 
Professor
Teaching Assistant #1
Teaching Assistant #2
Student 1 1.43 1.05 0.39
Student 2 -0.57 -1.33 0.87
Student 3 0.35 0.27 -0.94
Student 4 0.72 0.90 2.24
Student 5 -1.41 -1.23 -0.50
Student 6 0.10 0.27 0.56
Student 7 -2.04 -1.71 -0.94
Student 8 0.76 1.19 0.03
Student 9 0.47 0.56 -0.50
Student 10 0.18 0.03 -1.21
 
The professor is going to use the z-scores to calculate the correlation coefficient between his scores and those of his TAs. To calculate the correlation coefficient, he sums the products of the z-scores. The professor should divide this sum by     .
 
The professor constructed a table of correlation coefficients between his scores and those of his TAs. Select the correct missing correlation.
 
Professor
Teaching Assistant #1
Teaching Assistant #1      1
Teaching Assistant #2 0.36 0.31
 
Based on the correlation table, the professor should arrive at which of the following conclusions?
The professor and both of his TAs are well calibrated.
 
The two TAs are well calibrated with each other but not with the professor.
 
The professor and TA #1 are well calibrated, but TA #2 is off.
 
The professor and TA #2 are well calibrated, but TA #1 is off.
 
 
The professor thinks TA #1 may be too generous in her grading and decides to subtract 2 points from each student’s grade from TA #1 before converting the scores to z-scores and computing the Pearson correlation coefficient between her grades, the professor’s grades, and those of TA #2. This change in the TA #1’s scores will      the correlation between the TA #1’s scores and the professor’s and TA #2’s scores.
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