Imagine that a professor of psychology has two teaching assistants (TAs) who will help her grade assignments for the duration of the semester. The professor wants to make sure that she and the TAs are well calibrated with one another, so she has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, she 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 her class for each grader. Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 0.70 1.27 1.27 Student 2 0.83 -0.64 -1.55 Student 3 -0.98 0.38 -0.14 Student 4 2.21 0.80 0.92 Student 5 -0.54 -1.34 -1.06 Student 6 0.43 0.10 0.30 Student 7 -1.03 -2.09 -1.50 Student 8 -0.01 0.85 1.14 Student 9 -0.54 0.48 0.57 Student 10 -1.07 0.20 0.04 The professor is going to use the z-scores to calculate the correlation coefficient between her scores and those of her TAs. To calculate the correlation coefficient, she sums the products of the z-scores. The professor should divide this sum by . The professor constructed a table of correlation coefficients between her scores and those of her TAs. Select the correct missing correlation. Professor Teaching Assistant #1 Teaching Assistant #1 1 Teaching Assistant #2 0.37 0.91 Based on the correlation table, the professor should arrive at which of the following conclusions? The professor and both of her 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 she tends to be a harsh grader and decides to add 5 points to each student’s grade before converting the scores to z-scores and computing the Pearson correlation coefficient between her grades and the two teaching assistants’. This change in the professor’s scores will the correlation between the professor’s scores and

Imagine that a professor of psychology has two teaching assistants (TAs) who will help her grade assignments for the duration of the semester. The professor wants to make sure that she and the TAs are well calibrated with one another, so she has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, she 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 her class for each grader. Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 0.70 1.27 1.27 Student 2 0.83 -0.64 -1.55 Student 3 -0.98 0.38 -0.14 Student 4 2.21 0.80 0.92 Student 5 -0.54 -1.34 -1.06 Student 6 0.43 0.10 0.30 Student 7 -1.03 -2.09 -1.50 Student 8 -0.01 0.85 1.14 Student 9 -0.54 0.48 0.57 Student 10 -1.07 0.20 0.04 The professor is going to use the z-scores to calculate the correlation coefficient between her scores and those of her TAs. To calculate the correlation coefficient, she sums the products of the z-scores. The professor should divide this sum by . The professor constructed a table of correlation coefficients between her scores and those of her TAs. Select the correct missing correlation. Professor Teaching Assistant #1 Teaching Assistant #1 1 Teaching Assistant #2 0.37 0.91 Based on the correlation table, the professor should arrive at which of the following conclusions? The professor and both of her 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 she tends to be a harsh grader and decides to add 5 points to each student’s grade before converting the scores to z-scores and computing the Pearson correlation coefficient between her grades and the two teaching assistants’. This change in the professor’s scores will the correlation between the professor’s scores and

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Question

	Professor	Teaching Assistant #1	Teaching Assistant #2
Student 1	0.70	1.27	1.27
Student 2	0.83	-0.64	-1.55
Student 3	-0.98	0.38	-0.14
Student 4	2.21	0.80	0.92
Student 5	-0.54	-1.34	-1.06
Student 6	0.43	0.10	0.30
Student 7	-1.03	-2.09	-1.50
Student 8	-0.01	0.85	1.14
Student 9	-0.54	0.48	0.57
Student 10	-1.07	0.20	0.04

The professor is going to use the z-scores to calculate the correlation coefficient between her scores and those of her TAs. To calculate the correlation coefficient, she sums the products of the z-scores. The professor should divide this sum by .

The professor constructed a table of correlation coefficients between her scores and those of her TAs. Select the correct missing correlation.

	Professor	Teaching Assistant #1
Teaching Assistant #1		1
Teaching Assistant #2	0.37	0.91

Based on the correlation table, the professor should arrive at which of the following conclusions?

The professor and both of her 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 she tends to be a harsh grader and decides to add 5 points to each student’s grade before converting the scores to z-scores and computing the Pearson correlation coefficient between her grades and the two teaching assistants’. This change in the professor’s scores will the correlation between the professor’s scores and TA #1’s and TA #2’s scores.

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