**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 \( \alpha = 0.05 \).

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**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 \( \alpha = 0.05 \).
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.

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