Fill out this paragraph if a posthoc analysis is appropriate.) A posthoc analysis using ___________________. was done to determine which of the three classroom environments had a different mean test score. Based on the results of the test, the classroom environments which provided different mean test scores are _______________________..   Suppose you are a school administrator and you are looking for ways to boost the learning environment of your students, what actions can you take based on the results of the study?

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In this study, the college instructor aims to know whether there are differences in the performance of students among the three classroom environments. We consider the three classroom environments (Mozart’s piece, relaxation music, and silence) as the factor variable. Also, the response variable is the performance of the students which is in the ratio level of measurement. The students were independently and randomly assigned to each of the three classroom environments: Mozart piece, relaxation music, and silence.

 

The p-values obtained from the Shapiro-Wilk test indicate that the assumption of normality was satisfied. Further, results obtained from the Levene’s test indicate that the assumption of homogeneity of variances was satisfied. Considering the variable of interest and the results of the test for the assumptions, the appropriate test procedure to analyze the given data is the Kruskal Wallis Test.

 

The appropriate set of hypotheses to test the given objective is Ho: There is no significant difference in the performance of the students among the three classroom environments  and Ha: There is a significant difference in the performance of the students among three classroom environments. The test yield a p-value equal to 0.000000006479. Thus, we can infer that we have sufficient evidence to say that there is a significant difference in the performance of the students among three classroom environments. Given this result, we can proceed with a posthoc analysis.

 

(Fill out this paragraph if a posthoc analysis is appropriate.)

A posthoc analysis using ___________________. was done to determine which of the three classroom environments had a different mean test score. Based on the results of the test, the classroom environments which provided different mean test scores are _______________________..

 

Suppose you are a school administrator and you are looking for ways to boost the learning environment of your students, what actions can you take based on the results of the study?

_____________________________

PROBLEM 5: Can music help you study?
The sound waves produced by the music that we hear reach our brain by converting them into
electrical signals which then travel to the eighth cranial nerve of our brain. Have you tried listening
to music while studying? In the early 1990s, an experiment by Raucher and his colleagues revealed
that listening to classical music could improve memory.
So, does listening to music help or hinder students' learning? A college instructor wishes to test this so-called
"Mozart Effect" on a random sample of 45 students. Each randomly selected student was assigned to study in
a classroom under a certain environment (Classrooms A, B, and C). The students were then given a
memorization task to be accomplished within 10 minutes. While performing the task, the students in Classroom
A listened to a Mozart piece, students in Classroom B listened to relaxation music, and students in Classroom
C sat in silence. At the end of the task, the students were given a 20-item test and their scores were recorded.
R COMMANDER OUTPUT #5.1
R COMMANDER OUTPUT #5.2
Shapiro-Wilk normality test
Levene's Test
data:
for Homogeneity of Variance
Df F value Pr (>F)
group 2 0.5473 0.5826
score
w = 0.90955, p-value = 0.1333
w = 0.92179, p-value = 0.2051
w = 0.93674, p-value = 0.3431
classroom = A
classroom = B
classroom = C
42
R COMMANDER OUTPUT #5.3
R COMMANDER OUTPUT #5.4
Parametric test
Df Sum Sq Mean Sq F value Pr (>F)
sd data:n
mean
A 18.33333 1.175139
B 15.06667 1.222799
C 10.73333 1.533747
15
classroom
2
436.0
218.02
125.1 <2e-16
15
Residuals
42
73.2
1.74
15
Transcribed Image Text:PROBLEM 5: Can music help you study? The sound waves produced by the music that we hear reach our brain by converting them into electrical signals which then travel to the eighth cranial nerve of our brain. Have you tried listening to music while studying? In the early 1990s, an experiment by Raucher and his colleagues revealed that listening to classical music could improve memory. So, does listening to music help or hinder students' learning? A college instructor wishes to test this so-called "Mozart Effect" on a random sample of 45 students. Each randomly selected student was assigned to study in a classroom under a certain environment (Classrooms A, B, and C). The students were then given a memorization task to be accomplished within 10 minutes. While performing the task, the students in Classroom A listened to a Mozart piece, students in Classroom B listened to relaxation music, and students in Classroom C sat in silence. At the end of the task, the students were given a 20-item test and their scores were recorded. R COMMANDER OUTPUT #5.1 R COMMANDER OUTPUT #5.2 Shapiro-Wilk normality test Levene's Test data: for Homogeneity of Variance Df F value Pr (>F) group 2 0.5473 0.5826 score w = 0.90955, p-value = 0.1333 w = 0.92179, p-value = 0.2051 w = 0.93674, p-value = 0.3431 classroom = A classroom = B classroom = C 42 R COMMANDER OUTPUT #5.3 R COMMANDER OUTPUT #5.4 Parametric test Df Sum Sq Mean Sq F value Pr (>F) sd data:n mean A 18.33333 1.175139 B 15.06667 1.222799 C 10.73333 1.533747 15 classroom 2 436.0 218.02 125.1 <2e-16 15 Residuals 42 73.2 1.74 15
R COMMANDER OUTPUT #5.5
Parametric posthoc analysis
Linear Hypotheses:
Estimate Sstd. Error t value
Pr (>|t|)
в
- A == 0
-3.2667
0.4821
-6.776 <0.000001
C -
A == 0
-7.6000
0.4821 -15.766 <0.000001
c - B == 0 -4.3333
0.4821
-8.989 <0.000001
R COMMANDER OUTPUT #5.6
R COMMANDER OUTPUT #5.6
Nonparametric posthoc analysis
Comparison of x by group
(No adjustment)
Nonparametric test
data:
score by classroom
Kruskal-Wallis chi-squared = 37.709,
df = 2, p-value = 0.000000006479
Col Mean-|
Row Mean |
A
B
3.017854
0.0013*
6.140495
3.122641
0.0000*
0.0009*
Transcribed Image Text:R COMMANDER OUTPUT #5.5 Parametric posthoc analysis Linear Hypotheses: Estimate Sstd. Error t value Pr (>|t|) в - A == 0 -3.2667 0.4821 -6.776 <0.000001 C - A == 0 -7.6000 0.4821 -15.766 <0.000001 c - B == 0 -4.3333 0.4821 -8.989 <0.000001 R COMMANDER OUTPUT #5.6 R COMMANDER OUTPUT #5.6 Nonparametric posthoc analysis Comparison of x by group (No adjustment) Nonparametric test data: score by classroom Kruskal-Wallis chi-squared = 37.709, df = 2, p-value = 0.000000006479 Col Mean-| Row Mean | A B 3.017854 0.0013* 6.140495 3.122641 0.0000* 0.0009*
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