Imagine that a professor of psychology has two teaching assistants (TAs) who wil
ID: 3266872 • Letter: I
Question
Imagine that a professor of psychology 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 population of 10 students in his class for each grader. The professor is going to use the z-scores to calculate the Pearson correlation coefficient between his scores and those of his TAs. To calculate the Pearson 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. Based on the correlation table, the professor should arrive at which of the following conclusions? The TAs are well calibrated with each other but not with the professor. The professor and TA #2 are well calibrated, but TA #1 is off. The professor and TA #1 are well calibrated, but TA #2 is off. The professor and both of his TAs are well calibrated. 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.Explanation / Answer
According the formula, th eprofessor showuld divide the sum by N=10.
r=sigma zx zy/N
Usig given information, product of z scores for professor and teaching assistant 1 are as follows:
0.5080, -0.5429, -0.3441, 1.7628, 0.6223, 0.0539, 2.1049, 0.0328, -0.2499, -0.2400
The sum of products is 3.708
The Pearson correlation coeffciient, r=3.708/10=0.3708.
Because, there is high correlation between TA2 and professor (0.91), they are well calibrated, but TA1 and professor has poor correlation (0.3708), hence they are not well calibrated. Therefore, professor and both of hi sTA s are not well calibrated. TA1 and TA2 has correlation value of 0.25, so they are not all well calibrated. Thus, option 2 is correct.