The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At α=​0.01, is there enough evidence to conclude that their scores improved the second time they took the​ test? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (f).   Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14   Score on first test 468 459 572 449 586 598 393 320 586 525 355 328 470 400   Score on second testScore on second test 473 468 588 495 560 614 328 329 588 531 404 344 520 429   ​(a) Identify the claim and state Upper H 0H0and Upper H Subscript aHa.

Question
The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At α=​0.01, is there enough evidence to conclude that their scores improved the second time they took the​ test? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (f).
 
Student
1
2
3
4
5
6
7
8
9
10
11
12
13
14
 
Score on first test
468
459
572
449
586
598
393
320
586
525
355
328
470
400
 
Score on second testScore on second test
473
468
588
495
560
614
328
329
588
531
404
344
520
429
 
​(a) Identify the claim and state Upper H 0H0
and Upper H Subscript aHa.

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