**Knowledge Check 3: ANOVA Analysis** **Directions:** Answer each question fully and to the best of your ability. 1. An education researcher is comparing four different algebra curricula. Eighth grade students are randomly assigned to one of the four groups with each group consisting of 20 students. Their state achievement test scores are compared at the end of the year. a. In this context, construct the ANOVA model. - \( k = 4 \) - \( n = 4 \cdot 20 = 80 \) - \( \text{df (between)} = k - 1 = 4 - 1 = 3 \) - \( \text{df (within)} = n - k = 80 - 4 = 76 \) - \( \text{total df = df (between) + df (within)} = 3 + 76 = 79 \) - Total sum of squares: \( 829 + 47511.38 = 48340.38 \) - MS (between) = SS (between) / df (between) \[ = \frac{829}{3} = 276.3333 \] - MS (within) = SS (within) / df (within) \[ = \frac{47511.38}{76} = 625.1497 \] - \( F \) statistic calculation: \[ F = \frac{\text{MS (between)}}{\text{MS (within)}} = \frac{276.3333}{625.1497} = 0.4420 \] b. **ANOVA Table Completion:** | Source | df | SS | MS | F | |-----------------|----|---------|----------|--------| | Between Groups | 3 | 829 | 276.3333 | 0.4420 | | Within Groups | 76 | 47511.38| 625.1497 | | | Total | 79 | 48340.38| | | c. **Statistical Test:** Use the appropriate statistical procedure to determine whether the curricula differ with respect to math achievement. Use \( \alpha = 0.05 \).
**Knowledge Check 3: ANOVA Analysis** **Directions:** Answer each question fully and to the best of your ability. 1. An education researcher is comparing four different algebra curricula. Eighth grade students are randomly assigned to one of the four groups with each group consisting of 20 students. Their state achievement test scores are compared at the end of the year. a. In this context, construct the ANOVA model. - \( k = 4 \) - \( n = 4 \cdot 20 = 80 \) - \( \text{df (between)} = k - 1 = 4 - 1 = 3 \) - \( \text{df (within)} = n - k = 80 - 4 = 76 \) - \( \text{total df = df (between) + df (within)} = 3 + 76 = 79 \) - Total sum of squares: \( 829 + 47511.38 = 48340.38 \) - MS (between) = SS (between) / df (between) \[ = \frac{829}{3} = 276.3333 \] - MS (within) = SS (within) / df (within) \[ = \frac{47511.38}{76} = 625.1497 \] - \( F \) statistic calculation: \[ F = \frac{\text{MS (between)}}{\text{MS (within)}} = \frac{276.3333}{625.1497} = 0.4420 \] b. **ANOVA Table Completion:** | Source | df | SS | MS | F | |-----------------|----|---------|----------|--------| | Between Groups | 3 | 829 | 276.3333 | 0.4420 | | Within Groups | 76 | 47511.38| 625.1497 | | | Total | 79 | 48340.38| | | c. **Statistical Test:** Use the appropriate statistical procedure to determine whether the curricula differ with respect to math achievement. Use \( \alpha = 0.05 \).
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.4: Scatter Plots And Line Of Fit
Problem 14HP
Related questions
Topic Video
Question
looking for help with c
![**Knowledge Check 3: ANOVA Analysis**
**Directions:** Answer each question fully and to the best of your ability.
1. An education researcher is comparing four different algebra curricula. Eighth grade students are randomly assigned to one of the four groups with each group consisting of 20 students. Their state achievement test scores are compared at the end of the year.
a. In this context, construct the ANOVA model.
- \( k = 4 \)
- \( n = 4 \cdot 20 = 80 \)
- \( \text{df (between)} = k - 1 = 4 - 1 = 3 \)
- \( \text{df (within)} = n - k = 80 - 4 = 76 \)
- \( \text{total df = df (between) + df (within)} = 3 + 76 = 79 \)
- Total sum of squares: \( 829 + 47511.38 = 48340.38 \)
- MS (between) = SS (between) / df (between)
\[
= \frac{829}{3} = 276.3333
\]
- MS (within) = SS (within) / df (within)
\[
= \frac{47511.38}{76} = 625.1497
\]
- \( F \) statistic calculation:
\[
F = \frac{\text{MS (between)}}{\text{MS (within)}} = \frac{276.3333}{625.1497} = 0.4420
\]
b. **ANOVA Table Completion:**
| Source | df | SS | MS | F |
|-----------------|----|---------|----------|--------|
| Between Groups | 3 | 829 | 276.3333 | 0.4420 |
| Within Groups | 76 | 47511.38| 625.1497 | |
| Total | 79 | 48340.38| | |
c. **Statistical Test:** Use the appropriate statistical procedure to determine whether the curricula differ with respect to math achievement. Use \( \alpha = 0.05 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0259c9da-a893-42a4-9aeb-f2e84d3b7404%2F8bb61596-eb96-4f6b-811a-3e3a5c60305b%2Frzc617b.jpeg&w=3840&q=75)
Transcribed Image Text:**Knowledge Check 3: ANOVA Analysis**
**Directions:** Answer each question fully and to the best of your ability.
1. An education researcher is comparing four different algebra curricula. Eighth grade students are randomly assigned to one of the four groups with each group consisting of 20 students. Their state achievement test scores are compared at the end of the year.
a. In this context, construct the ANOVA model.
- \( k = 4 \)
- \( n = 4 \cdot 20 = 80 \)
- \( \text{df (between)} = k - 1 = 4 - 1 = 3 \)
- \( \text{df (within)} = n - k = 80 - 4 = 76 \)
- \( \text{total df = df (between) + df (within)} = 3 + 76 = 79 \)
- Total sum of squares: \( 829 + 47511.38 = 48340.38 \)
- MS (between) = SS (between) / df (between)
\[
= \frac{829}{3} = 276.3333
\]
- MS (within) = SS (within) / df (within)
\[
= \frac{47511.38}{76} = 625.1497
\]
- \( F \) statistic calculation:
\[
F = \frac{\text{MS (between)}}{\text{MS (within)}} = \frac{276.3333}{625.1497} = 0.4420
\]
b. **ANOVA Table Completion:**
| Source | df | SS | MS | F |
|-----------------|----|---------|----------|--------|
| Between Groups | 3 | 829 | 276.3333 | 0.4420 |
| Within Groups | 76 | 47511.38| 625.1497 | |
| Total | 79 | 48340.38| | |
c. **Statistical Test:** Use the appropriate statistical procedure to determine whether the curricula differ with respect to math achievement. Use \( \alpha = 0.05 \).
Expert Solution
Step 1
The null and alternative hypotheses are,
H0: There is no significant difference between four different algebra curricula with respect to math achievement.
H1: There is significant difference between four different algebra curricula with respect to math achievement.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL