The following data give SAT mean scores for math by state for 1989 and 1999 for 20 randomly selected states (source: The World Almanac and Book of Facts 2000).
|
State
|
1989
|
1999
|
|
Arizona
|
523
|
525
|
|
Connecticut
|
498
|
509
|
|
Alabama
|
539
|
555
|
|
Indiana
|
487
|
498
|
|
Kansas
|
561
|
576
|
|
Oregon
|
509
|
525
|
|
Nebraska
|
560
|
571
|
|
New York
|
496
|
502
|
|
Virginia
|
507
|
499
|
|
Washington
|
515
|
526
|
|
Illinois
|
539
|
585
|
|
North Carolina
|
469
|
493
|
|
Georgia
|
475
|
482
|
|
Nevada
|
512
|
517
|
|
Ohio
|
520
|
568
|
|
New Hampshire
|
510
|
518
|
Assuming that the samples come from a normal distribution:
(a) Test that the mean SAT score for math in 1999 is greater than that in 1989 at α = 0.05. Assume the variances are equal.
(b) Test for the equality of the variances at α = 0.05.