Question

An agency offers preparation courses for a graduate school admissions test to students. As part of an experiment to evaluate the merits of the​ course, 40 students were chosen and divided into 20 pairs in such a way that the members of any pair had similar academic records. Before taking the​ test, one member of each pair was assigned at random to take the preparation​ course, while the other member did not take a course. The achievement test scores are contained in the accompanying table. Assuming that the differences in scores follow a normal​ distribution, test at the

1010​%

​level, the null hypothesis that the two population means are equal against the alternative that the true mean is higher for students taking the preparation course.

Let

mu 1μ1

be the mean test scores for those who took the preparation course 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 correct answer 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 test statistic is

BETWEEN -tn-1,a/2 and tn-1,a/2.  /LESS THAN -tn-1,a. / LESS THAN -tn-1,a/2.  /GREATER THAN tn-1,a/2.  /GREATER THAN -tn-1,a. /GREATER THAN tn-1,a.  /LESS THAN tn-1,a.=? There is SUFFİCİENT/UNSUFFİCİENT=? evidence that the true mean is higher for students taking the preparation

course.

ACHİEVEMENT 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 CRİTİCAL VALUES OF STUDENT'S t DİSTRİBUTİON

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

Answer 1