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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
Kansas
561
576
Oregon
Nebraska
560
571
New York
496
502
Virginia
507
499
Washington
515
526
Illinois
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.
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