The table below shows the critical reading scores for 14 students the first two

Question

The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At a=0.01, is there enough evidence to conclude that their scores improved the second time they took the test?

Student   Score on first test   Score on second test

1   344   352

2   356   379

3   445   461

4   407   422

5   594   584

6   359   408

7   452   382

8   494   517

9   555   567

10   572   580

11   510   555

12   605   642

13   396   411

14   392   402

1. Identify the claim and state H0 and Ha

2. Find the critical values & identify the rejection regions.

3. Calculate d and sd

4. Use the t-test to find the standardized the test statistic t

5. Decide whether to reject or fail to reject the null hypothesis

Explanation / Answer

1) ho: there is no significant difference in the mean scores of 2 test h1: mean score in 2nd test is greater than that of 1st test 2) critical value t(a,n-2) =(T.INV(0.01,13)) -2.650308838 values less than -2.65 lie in the ciritcal region 3) d_mean -12.9286 d_sd 28.54272 4) t =(mean_diff)/(sd_diff/sqrt(n)) =-12.92/(28.54/SQRT(14)) -1.693840695 5) since -t > -t(a,n-1), I fail to reject ho and conclude that there is no significant difference in the mean scores of 2 test 1st test 2nd test d 344 352 -8 356 379 -23 445 461 -16 407 422 -15 594 584 10 359 408 -49 452 382 70 494 517 -23 555 567 -12 572 580 -8 510 555 -45 605 642 -37 396 411 -15 392 402 -10

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