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
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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