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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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Student
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1
|
2
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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
|
|
and Upper H Subscript aHa.
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