AP Statistics / Mr. Hansen
Discussion Questions (10/6/2000)

Name: __________________________

1.

What percentage of the variation in the GPA of college freshmen is explained by variation in combined SAT scores? ____________ By other factors? ____________

2.

What name is given to the r² value you used in question 1?

3.

Which portion of the SAT, verbal or mathematical, does a better job of predicting college freshman performance as measured by GPA? ____________ Do you think this difference is statistically significant? ____________

4.

What is meant by the term statistically significant? _________________________

5.

Which is a better predictor of college freshman performance: high school GPA or combined SAT score? ____________ Why do you think selective colleges such as Harvard and Yale use the SAT as a selection criterion?

6.

The mean of the recentered (post-1995) SAT is 500 for each portion (verbal and mathematical), with a s.d. of 110 for each portion. What percentage of students scored 700 or above on the math SAT? ____________ What percentage of students scored between 300 and 500 on the verbal SAT? ____________ What verbal score would you need in order to be at the 95th percentile? ____________

7.

Two random variables (such as SAT math score and SAT verbal score) are said to be independent if their correlation is 0. For independent random variables, the variance of the sum equals the sum of the variances.

(a)

What is the variance of the math SAT? ____________ of verbal SAT? ____________

(b)

Is it valid to say that the variance of the SAT composite score equals the sum of the two answers you had for part (a)? Why or why not?

(c)

The s.d. of the SAT composite score is (circle one) 220, 14.832, 48400, 24200, 155.563, or none of the above.

8.

How were the r values in the table computed? _________________________ Is the r value for several merged data sets equal (in general) to the weighted average of the r values for the individual data sets? ____________ Why do you suppose the College Board used the methodology described in their Web page (http://www.collegeboard.org/index_this/sat/cbsenior/stats/stat030.html) for computing r values for the 48,039 freshmen in 23 colleges in 1995?