In a large statistics class, students have taken two exams. For each of the foll
ID: 3130658 • Letter: I
Question
In a large statistics class, students have taken two exams. For each of the following situations, report what you would expect for the value of the correlation coefficient between exam 1 score and exam 2 score. Give a brief justification for your answer.
1. Every student scores ten points higher on exam 2 than on exam 1.
2. Every student scores half as many points on exam 2 than on exam 1.
3. Every student guesses randomly on every question on both exams.
4. Every student scores twenty points less on exam 2 than on exam 1.
5. Every student scores 180 points for his/her combined score on the two exams.
Explanation / Answer
The linear correlation coefficient will be close to 1 if there is a strong linear relationship, and close to 0 if there is no relationship,
1. Every student scores ten points higher on exam 2 than on exam 1.
We expect it to be close to 1, as the relatiosnhip is strong and as one score increases, the other increases as well.
2. Every student scores half as many points on exam 2 than on exam 1.
We expect it to be close to 1, as the relatiosnhip is strong and as one score increases, the other increases as well.
3. Every student guesses randomly on every question on both exams.
We expect it to be close to 0, as the relatiosnhip is weak and unpredictable, as they are just guessing.
4. Every student scores twenty points less on exam 2 than on exam 1.
We expect it to be close to 1, as the relatiosnhip is strong and as one score increases, the other increases as well.
5. Every student scores 180 points for his/her combined score on the two exams.
We expect it to be close to -1, as the relatiosnhip is strong and as one score increases, the other decrease, as their sum is fixed.
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