Question

Kuya teaches a two-trimester course in Passionate Analysis Involving Numbers (PAIN). He would like to know if these students improved their scores in their second trimester of the course. Is there a significant difference in PAIN scores? Apparently a couple students were too 'pained' and dropped out after the first trimester (too bad so sad).

STUDENT	TRIMESTER 1	TRIMESTER 2
1	69	78
2	76	79
3	70	81
4	71
5	75	57
6	61	55
7	67	59
8	62
9	82	64
10	78	77
11	67	55
12	63	60
13	60	65
14	56
15	75	75
16	63	79
17	52	57
18	61	83
19	69	78
20	66	70
21	57	77
22	70	74
23	60	67
24	65	76
25	57	73
26	52	61
27	63	78
28	66	81
29	66	70
30	82	67
31	53	71
32	63	73

1. The appropriate test for this problem is:

t test for one sample

t test for dependent samples

t test for independent samples

one-way ANOVA

repeated measurements ANOVA

2. The obtained statistic value is:

0.44

– 0.44

- 2.21

2.21

3. The associated p value is:

.663

.331

.035

.018

4. Decision is:

reject the null

retain the null

5. Conclusion is:

second trimester’s scores are significantly higher than first trimester’s scores

first trimester’s scores are significantly higher than second trimester’s scores

no conclusion can be drawn

Answer 1

1)

option B)

t test for dependent samples

removing the rows in which data points were missing

using excel

t-Test: Paired Two Sample for Means
	TRIMESTER 1	TRIMESTER 2
Mean	65.79310345	70.34482759
Variance	66.09852217	75.87684729
Observations	29	29
Pearson Correlation	0.135692256
Hypothesized Mean Difference	0
df	28
t Stat	-2.212347221
P(T<=t) one-tail	0.017634836
t Critical one-tail	1.701130934
P(T<=t) two-tail	0.035269672
t Critical two-tail	2.048407142

2)

TS = -2.21

option C)

3)

this is one-tailed test

p-value = 0.018

option D)

4)

we reject the null as p-value < 0.05 (alpha)

5)

A) second trimester’s scores are significantly higher than first trimester’s scores

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