STATISTICAL METHODS
Second Exam
One-Way Analysis of Variance
Problem 1. EQUAL REPLICATIONS
At the beginning of the school year, Anislag National High School teachers were asked to conduct Regional Diagnostic
Assessment to plan for class intervention. The teachers administer to students a 60 item test. After the research, the
Administrative Assistant is tasked to consolidate the average scores of the assessment of Elementary and Junior High School grade
level for compliance to the Division Office. The data are presented in Table 1. In order to test the hypothesis if there is no
significant difference in the meantime of student’s average scores among the Elementary and Junior High School grade level.
Assume the populations to be approximately normal and have equal variance.
Table 1. The average scores of Elementary and Junior High School students on their Regional Diagnostic Assessment as
affected by different grade level
GRADE LEVEL SCORES
1 2 3 4 5
Grade 1 55 50 48 43 60
Grade 2 56 51 42 41 45
Grade 3 58 45 60 42 47
Grade 4 45 60 60 52 48
Grade 5 48 60 60 60 50
Grade 6 60 52 58 40 60
Grade 7 60 50 55 52 58
Grade 8 59 55 50 57 60
Grade 9 55 57 51 60 55
Grade 10 60 58 53 60 59
Problem 2. UNEQUAL REPLICATIONS
At the beginning of the school year, Anislag National High School teachers were asked to conduct Regional Diagnostic
Assessment to plan for class intervention. The teachers administer to students a 60 item test. After the research, the
Administrative Assistant is tasked to consolidate the average scores of the assessment of Elementary and Junior High School grade
level for compliance to the Division Office. The obtained average scores of students were not completed due to delays caused by
the Covid-19 pandemic. The data are presented in Table 1. In order to test the hypothesis if there is no significant difference in the
meantime of student’s average scores among the Elementary and Junior High School grade level. Assume the populations to be
approximately normal and have equal variances.
Table 1. The average scores of Elementary and Junior High School students on their Regional Diagnostic Assessment as
affected by different grade level
GRADE LEVEL SCORES
1 2 3 4 5
Grade 1 55 50 48 43 60
Grade 2 56 51 42 41
Grade 3 58 45 60 42 47
Grade 4 45 60 60 52
Grade 5 48 60 60 60
Grade 6 60 52 58 40 60
Grade 7 60 50 55
Grade 8 59 55 50 57 60
Grade 9 55 57 51 60
Grade 10 60 58 53 60 59
Second Exam
One-Way Analysis of Variance
Problem 1. EQUAL REPLICATIONS
At the beginning of the school year, Anislag National High School teachers were asked to conduct Regional Diagnostic
Assessment to plan for class intervention. The teachers administer to students a 60 item test. After the research, the
Administrative Assistant is tasked to consolidate the average scores of the assessment of Elementary and Junior High School grade
level for compliance to the Division Office. The data are presented in Table 1. In order to test the hypothesis if there is no
significant difference in the meantime of student’s average scores among the Elementary and Junior High School grade level.
Assume the populations to be approximately normal and have equal variance.
Table 1. The average scores of Elementary and Junior High School students on their Regional Diagnostic Assessment as
affected by different grade level
GRADE LEVEL SCORES
1 2 3 4 5
Grade 1 55 50 48 43 60
Grade 2 56 51 42 41 45
Grade 3 58 45 60 42 47
Grade 4 45 60 60 52 48
Grade 5 48 60 60 60 50
Grade 6 60 52 58 40 60
Grade 7 60 50 55 52 58
Grade 8 59 55 50 57 60
Grade 9 55 57 51 60 55
Grade 10 60 58 53 60 59
Problem 2. UNEQUAL REPLICATIONS
At the beginning of the school year, Anislag National High School teachers were asked to conduct Regional Diagnostic
Assessment to plan for class intervention. The teachers administer to students a 60 item test. After the research, the
Administrative Assistant is tasked to consolidate the average scores of the assessment of Elementary and Junior High School grade
level for compliance to the Division Office. The obtained average scores of students were not completed due to delays caused by
the Covid-19 pandemic. The data are presented in Table 1. In order to test the hypothesis if there is no significant difference in the
meantime of student’s average scores among the Elementary and Junior High School grade level. Assume the populations to be
approximately normal and have equal variances.
Table 1. The average scores of Elementary and Junior High School students on their Regional Diagnostic Assessment as
affected by different grade level
GRADE LEVEL SCORES
1 2 3 4 5
Grade 1 55 50 48 43 60
Grade 2 56 51 42 41
Grade 3 58 45 60 42 47
Grade 4 45 60 60 52
Grade 5 48 60 60 60
Grade 6 60 52 58 40 60
Grade 7 60 50 55
Grade 8 59 55 50 57 60
Grade 9 55 57 51 60
Grade 10 60 58 53 60 59
