IV. Results A. Based on your results, determine whether the data provide evidenc
ID: 3268204 • Letter: I
Question
IV. Results
A. Based on your results, determine whether the data provide evidence for a valid effect.
B. Explain whether or not the results are statistically significant. Support your response with results from the data analysis.
C. Present properly labeled graphs representing the data analysis results detailed clearly for ease of stakeholder interpretation.
The question was investigated of whether pleasant aromas help a student learn better. All 21 participants learned both under a condition of smelling nothing and under a condition of smelling a floral scent. Counterbalancing was followed so that some participants learned without the scent first and some learned with the scent first. All participants were apprised that the scents were “safe” and that if they wished they could leave the study at any time. Data in terms of “time (in seconds) to complete a pencil and paper maze” are shown below:
Unscented-Trial Scented-Trial 38.4 53.1 46.2 54.7 72.5 74.2 38 49.6 82.8 53.6 33.9 51.3 50.4 44.1 35 34 32.8 34.5 60.1 59.1 75.1 67.3 57.6 75.5 55.5 41.1 49.5 52.2 40.9 28.3 44.3 74.9 93.8 77.5 47.9 50.9 75.2 70.1 46.2 60.3 56.3 59.9Explanation / Answer
Part (A & B)
Let X = reduction in “time (in seconds) to complete a pencil and paper maze”
= “time (in seconds) to complete a pencil and paper maze for unscented group participant” - “time (in seconds) to complete a pencil and paper maze for scented group participant”
Then, X ~ N(µ, 2) where 2 is unknown.
Claim: Pleasant aromas help a student learn better.
Hypotheses:
Null H0: µ = µ0 = 0 Vs
Alternative HA: µ > 0 [claim]
Test statistic:
t = (n)(Xbar - µ0)/s, where
Xbar = sample mean (given)
µ0 = 0
s = sample standard deviation
n = sample size = 21
So, tcal = - 0.537
Details of Excel calculations are tabulated below:
i
Unscented-Trial
Scented-Trial
xi
(xi - Xbar)
1
38.4
53.1
-14.7
-13.090476
2
46.2
54.7
-8.5
-6.8904762
3
72.5
74.2
-1.7
-0.0904762
4
38
49.6
-11.6
-9.9904762
5
82.8
53.6
29.2
30.809524
6
33.9
51.3
-17.4
-15.790476
7
50.4
44.1
6.3
7.9095238
8
35
34
1
2.6095238
9
32.8
34.5
-1.7
-0.0904762
10
60.1
59.1
1
2.6095238
11
75.1
67.3
7.8
9.4095238
12
57.6
75.5
-17.9
-16.290476
13
55.5
41.1
14.4
16.009524
14
49.5
52.2
-2.7
-1.0904762
15
40.9
28.3
12.6
14.209524
16
44.3
74.9
-30.6
-28.990476
17
93.8
77.5
16.3
17.909524
18
47.9
50.9
-3
-1.3904762
19
75.2
70.1
5.1
6.7095238
20
46.2
60.3
-14.1
-12.490476
21
56.3
59.9
-3.6
-1.9904762
Mean
-1.609524
sum(xi-Xbar)^2
3774.8581
s^2
188.7429
s
13.738373
tcal
-0.536873
tcrit
1.725
Distribution, Critical Value [level of significance is taken to be 5%]
Under H0, t ~ tn - 1
Critical value = upper 5% point of tn - 1.
tcrit = t20, 0.05 = 1.725
Decision Criterion (Rejection Region)
Reject H0, if tcal > tcrit .
Decision:
Since tcal (- 0.537) < tcrit (1.725), H0 is accepted
Conclusion:
There is not sufficient evidence to support the claim that the 'Pleasant aromas help a student learn better.'
Part (C)
The graphical representation could be any of the following:
Done
i
Unscented-Trial
Scented-Trial
xi
(xi - Xbar)
1
38.4
53.1
-14.7
-13.090476
2
46.2
54.7
-8.5
-6.8904762
3
72.5
74.2
-1.7
-0.0904762
4
38
49.6
-11.6
-9.9904762
5
82.8
53.6
29.2
30.809524
6
33.9
51.3
-17.4
-15.790476
7
50.4
44.1
6.3
7.9095238
8
35
34
1
2.6095238
9
32.8
34.5
-1.7
-0.0904762
10
60.1
59.1
1
2.6095238
11
75.1
67.3
7.8
9.4095238
12
57.6
75.5
-17.9
-16.290476
13
55.5
41.1
14.4
16.009524
14
49.5
52.2
-2.7
-1.0904762
15
40.9
28.3
12.6
14.209524
16
44.3
74.9
-30.6
-28.990476
17
93.8
77.5
16.3
17.909524
18
47.9
50.9
-3
-1.3904762
19
75.2
70.1
5.1
6.7095238
20
46.2
60.3
-14.1
-12.490476
21
56.3
59.9
-3.6
-1.9904762
Mean
-1.609524
sum(xi-Xbar)^2
3774.8581
s^2
188.7429
s
13.738373
tcal
-0.536873
tcrit
1.725
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