Question

The Testing Institute of Mind (TIM) claims to be able to significantly increase students' performance on a college admissions test with a one-day training program. A sample of 27 students took the test both before and after the training program. The spreadsheet shows the results for these students. Carry out a one-tailed t-test on H0: μ _Before ≥ μ _After (population mean of Before is greater than population mean of After) vs. Ha: μ _Before < μ _After (population mean of Before is less than population mean of After) at the α =.01

ID #	Before	After
1	392	415
2	334	345
3	378	396
4	470	480
5	473	473
6	443	436
7	459	473
8	426	422
9	493	525
10	382	380
11	473	474
12	394	401
13	513	525
14	483	482
15	480	482
16	440	438
17	439	451
18	435	431
19	451	440
20	495	501
21	526	529
22	473	483
23	440	452
24	481	473
25	459	450
26	399	387
27	452	449

a) what is the observed value of t?

a. -2.05

b. 2.05

c. 1.98

d. -1.98

B)  what is the critical value of t?

±2.49, ±2.48, -2.49, 2.48, 2.49

C) what is the probability (P) value of the test? (can you please break this down for me, I would like to be able to find out the values I am missing when I try to solve)

0.029, -0.026, 0.974, 0.026

D) what is the conclusion?

reject H0 and conclude the training is not effective

fail to reject H0 and conclude there is no evidence that training is effective

reject H0 and conclude the training is effective

fail to reject H0 and conclude the training is effective

Answer 1

In solution A Here Ho Mp 3 MA is Hi p < lla from the given data n=27 a = Ed = -4.07 sd = {(d-d) = 10.72 Test statutic to sols t= d = 407 = -1.98 10.72)527 B x=0.01, df = n-1=26 critical value = -2.479 =-2.18 o Pavalue = 0.029 D here P-value >0.01, so fail to reject Ho and conclude that there is no evidence that training is effective