An agency offers preparation courses for a graduate schooladmissions test to students. As part of an experiment to evaluatethe merits of the​ course, 40 students were chosen and divided into20 pairs in such a way that the members of any pair had similaracademic records. Before taking the​ test, one member of each pairwas assigned at random to take the preparation​ course, while theother member did not take a course. The achievement test scores arecontained in the accompanying table. Assuming that the differencesin scores follow a normal​ distribution, test at the
1010​%
​level, the null hypothesis that the two population means areequal against the alternative that the true mean is higher forstudents taking the preparation course.
Let
mu 1μ1
be the mean test scores for those who took the preparationcourse and let
mu 2μ2
be the mean test scores for those who did not take the course.Determine the null and alternative hypotheses. Choose the correctanswer below.
H0=?
H1=?
The test statistic is t=?
The critical​ value(s) is(are) =?
Determine the correct conclusion.
REJECT/DO NOT REJECT=? the null hypothesis since the teststatistic is
BETWEEN -tn-1,a/2 and tn-1,a/2.  /LESS THAN -tn-1,a. /LESS THAN -tn-1,a/2.  /GREATER THANtn-1,a/2.  /GREATER THAN -tn-1,a. /GREATER THANtn-1,a.  /LESS THAN tn-1,a.=? There isSUFFİCİENT/UNSUFFİCİENT=? evidence that the true mean is higher forstudents taking the preparation
course.
ACHÄ°EVEMENT TEST SCORES
| | | |
Sample | Took course | Did not take course | |
1 | | 7272 | 5858 | |
2 | | 6666 | 4949 | |
3 | | 6060 | 7878 | |
4 | | 7474 | 6161 | |
5 | | 8989 | 8383 | |
6 | | 6464 | 4646 | |
7 | | 7979 | 6868 | |
8 | | 8484 | 7676 | |
9 | | 7777 | 6565 | |
10 | | 8080 | 7070 | |
11 | | 7575 | 6262 | |
12 | | 8686 | 7979 | |
13 | | 6868 | 5252 | |
14 | | 9797 | 9595 | |
15 | | 8787 | 8080 | |
16 | | 9595 | 9292 | |
17 | | 7070 | 5555 | |
18 | | 8383 | 7474 | |
19 | | 8282 | 7373 | |
20 | | 9393 | 8989 |
UPPER CRÄ°TÄ°CAL VALUES OF STUDENT'S t DÄ°STRÄ°BUTÄ°ON
| DF | A = 0.1 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 | 0.0005 |
|---|
| ∞ | ta = 1.282 | 1.645 | 1.960 | 2.326 | 2.576 | 3.091 | 3.291 |
| 1 | 3.078 | 6.314 | 12.706 | 31.821 | 63.656 | 318.289 | 636.578 |
| 2 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | 22.328 | 31.600 |
| 3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 10.214 | 12.924 |
| 4 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | 7.173 | 8.610 |
| 5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | 5.894 | 6.869 |
| 6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | 5.208 | 5.959 |
| 7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | 4.785 | 5.408 |
| 8 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 | 4.501 | 5.041 |
| 9 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 | 4.297 | 4.781 |
| 10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 4.144 | 4.587 |
| 11 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 | 4.025 | 4.437 |
| 12 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 | 3.930 | 4.318 |
| 13 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 | 3.852 | 4.221 |
| 14 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 | 3.787 | 4.140 |
| 15 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 | 3.733 | 4.073 |
| 16 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 | 3.686 | 4.015 |
| 17 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 | 3.646 | 3.965 |
| 18 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 | 3.610 | 3.922 |
| 19 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 | 3.579 | 3.883 |
| 20 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 | 3.552 | 3.850 |
| 21 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 | 3.527 | 3.819 |
| 22 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 | 3.505 | 3.792 |
| 23 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 | 3.485 | 3.768 |
| 24 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 | 3.467 | 3.745 |
| 25 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 | 3.450 | 3.725 |
| 26 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 | 3.435 | 3.707 |
| 27 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 | 3.421 | 3.689 |
| 28 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 | 3.408 | 3.674 |
| 29 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 | 3.396 | 3.660 |
| 30 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 | 3.385 | 3.646 |
| 60 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 | 3.232 | 3.460 |
| 120 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 | 3.160 | 3.373 |
| 1000 | 1.282 | 1.646 | 1.962 | 2.330 | 2.581 | 3.098 | 3.300 |
