What are the alternate and null hypotheses? conclusion? Since the data above are
ID: 3360711 • Letter: W
Question
What are the alternate and null hypotheses?
conclusion?
Since the data above are in percent, what assumption of ANOVA is of concern in this analysis?
1. The data below involve 6 students each taking 3 tests: math, english, and science Are there significant differences between students or tests? Analyze these data with the appropriate ANOVA. Note the lack of replication in the data set Score (in percent) Student Math Engineering 68 74 89 90 84 82 89 87 Science 89 90 2 4 5 100 96 100 85 96 100 Analyze these data using the appropriate model of 2-way ANOVA. Give your results using standard format (the hypotheses and your conclusions relative to the hypotheses)Explanation / Answer
Solution:
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There are no any statistically significant differences between the students or tests.
Alternative hypothesis: Ha: There are statistically significant differences between the students or tests.
We assume 5% level of significance or = 0.05 for this test.
The two way ANOVA table is given as below:
(By using excel)
Student
Math
Engineering
Science
1
89
68
89
2
87
74
90
3
99
89
99
4
100
90
85
5
96
84
96
6
100
82
100
ANOVA: Two-Factor Without Replication
SUMMARY
Count
Sum
Average
Variance
1
3
246
82
147
2
3
251
83.66667
72.33333
3
3
287
95.66667
33.33333
4
3
275
91.66667
58.33333
5
3
276
92
48
6
3
282
94
108
Math
6
571
95.16667
33.36667
Engineering
6
487
81.16667
74.56667
Science
6
559
93.16667
36.56667
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Rows
476.5
5
95.3
3.873984
0.032594
3.325835
Columns
688
2
344
13.98374
0.001267
4.102821
Error
246
10
24.6
Total
1410.5
17
The p-value for rows or student is given as 0.0326 which is less than = 0.05, so we reject the null hypothesis.
The p-value for columns or subjects tests is given as 0.001267 which is less than = 0.05, so we reject the null hypothesis.
There is sufficient evidence to conclude that there are statistically significant differences between the students or tests.
The following assumption is required for the given ANOVA test.
For percentage data lying within the range 20 to 80%, we don’t need any transformation; otherwise we need square root transformation for the given data.
Student
Math
Engineering
Science
1
89
68
89
2
87
74
90
3
99
89
99
4
100
90
85
5
96
84
96
6
100
82
100
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