Date Due: Mon 10/11 or Thur 10/7                Value:  25 points [5 point penalty for each class late]

State's SAT Averages:  SAT Average versus Percent Taking Test

The August 31, 1992, issue of The Harrisburg Evening News lists the average SAT score for each of the fifty states and the percentage of high school seniors in the state who take the SAT test as indicated in the table below.
 

State	Average   SAT	% taking	State	Average   SAT	% taking	State	Average   SAT	% taking
Alabama	996	8	Maine	882	66	Oregon	925	55
Alaska	908	42	Maryland	907	66	Pennsylvania	877	68
Arizona	933	27	Massachusetts	902	80	Rhode Island	881	70
Arkansas	990	6	Michigan	987	11	South Carolina	831	59
California	900	46	Minnesota	1053	10	South Dakota	1040	6
Colorado	960	29	Mississippi	1004	4	Tennessee	1013	13
Connecticut	900	79	Missouri	1004	11	Texas	876	44
Delaware	895	66	Montana	988	24	Utah	1041	5
Florida	884	50	Nebraska	1018	11	Vermont	897	69
Georgia	842	65	Nevada	922	27	Virginia	893	63
Hawaii	878	56	New Hampshire	923	76	Washington	916	50
Idaho	963	17	New Jersey	891	75	West Virginia	924	17
Illinois	1010	15	New Mexico	996	12	Wisconsin	1029	11
Indiana	868	58	New York	882	75	Wyoming	978	13
Iowa	1096	5	North Carolina	855	57
Kansas	1033	10	North Dakota	1068	6
Kentucky	988	11	Ohio	951	23
Louisiana	991	9	Oklahoma	1007	9

 
I.  Predict:  Answer the following WITHOUT studying the data - use only your intuition.
    a)  Do you think there is a relationship between a states average SAT score and the % of the seniors who take the test?
    b)  If you think there is a relationship is it positive or negative?

II.  Analyze the relationship
    a)  Use your calculator to draw a scatter plot of the SAT score (x) versus the % (y), and make a rough sketch of the plot by hand.
    b)  Use your calculator to find the Correlation Coefficient r.
    c)  Use your calculator to find the regression line   y = ax + b
    d)  Is the linear relationship significant?  Why?
    e)  Predict the percent taking the SAT if the SAT average score is 1000.

Teaching Evaluations    Class size versus Course Evaluations

Investigate whether there seems to be an association between the number of students in a class and the students' average rate of the the instructor on the course evaluation.  The following table lists these variables for 25 courses taught by an instructor over a six year period.  The students' ratings of the instructor are on a scale of 1 to 9.
 

Course	Number of Students	Average Rating	Course	Number of Students	Average Rating	Course	Number of Students	Average Ratings
1	11	6.7	10	24	5.3	19	10	8.5
2	12	5.9	11	20	6.7	20	24	7.8
3	21	6.8	12	24	7.8	21	5	7.8
4	32	5.3	13	20	5.7	22	23	7.3
5	23	5.2	14	17	6.5	23	12	7.3
6	13	7.2	15	23	6.4	24	21	7.0
7	20	5.0	16	17	6.4	25	8	7.9
8	20	5.5	17	13	7.6
9	8	6.5	18	20	6.9

I.  Predict:  Answer the following WITHOUT studying the data - use only your intuition.
    a)  Do you think there is a relationship between class size and the student's average rate of an instructor.
    b)  If you think there is a relationship is it positive or negative?

II.  Analyze the relationship
    a)  Use your calculator to draw a scatter plot of the class size (x) versus evaluation (y), and make a rough sketch of the plot by hand.
    b)  Use your calculator to find the Correlation Coefficient r.
    c)  Use your calculator to find the regression line   y = ax + b
    d)  Is the linear relationship significant?  Why?
    e)  Predict:
            i)  the average evaluation for a class size of 25.
            ii)  the average evaluation for a class size of 50.
            iii)  Are the above two predictions equally dependable?  Discuss?