Question

Trosset chapter 15.7 exercise 8.

A class of 35 students took two midterm tests. Jack missed the first test and Jill missed the second test. The 33 students who took both tests scored an average of 75 points on the first test, with a standard deviation of 10 points, and an average of 64 points on the second test, with a standard deviation of 12 points. The scatter diagram of their scores is roughly ellipsoidal, with a correlation coefficient of r = 0.5. Because Jack and Jill each missed one of the tests, their professor needs to guess how each would have performed on the missing test in order to compute their semester grades. Jill scored 80 points on Test 1. She suggests that her missing score on Test 2 be replaced with her score on Test 1, 80 points. What do you think of this suggestion? What score would you advise the professor to assign? Jack scored 76 points on Test 2, precisely one standard deviation above the Test 2 mean. He suggests that his missing score on Test 1 be replaced with a score of 85 points, precisely one standard deviation above the Test 1 mean. What do you think of this suggestion? What score would you advise the professor to assign?

Answer 1

What we can do is, we can find the linear regression line that relates the scores in two test. The correlation coefficient is moderate, so this is a good option to do.

The linear equation is of the form

Let First Test be the X variable :

The second test be the Y variable :

Now if Jill scored 80 points in the first test, that means X=80

then

Her suggestion is overvalued.

She would have scored 67 in test 2

We would advise the professor to assign 67 to Jill.

Now for Jack let X variable be Test 2 and Y variable be Test 1 score

Jack scored X=76 in test 2

The suggestion is over valued.

We would advise the professor to assign 80.04 to Jack