A. State the Null and Alternate Hypotheses B. Compute the F-ratio and make a decision using an a = .05 c. Compute and interpret the effect size for this experiment

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**Mood Score Data from Yoga Class Study**

In this study, volunteers participated in a yoga class three times per week for three weeks. Mood scores for three participants were collected weekly and are presented in the table below.

| Subject | Week 1 | Week 2 | Week 3 | P-totals |
|---------|--------|--------|--------|----------|
| A       | 3      | 4      | 5      | 12       |
| B       | 1      | 4      | 6      | 11       |
| C       | 2      | 1      | 6      | 9        |

**Summary Statistics:**
- For Subject B: 
  - Total (T) = 15
  - Sum of Squares (SS) = 2
- For Subject C:
  - Total (T) = 15
  - Sum of Squares (SS) = 2
- Grand Total (G) = 27
- Sum of all squared scores (Σx²) = 108

**Analysis Tasks:**

A. **State the Null and Alternate Hypotheses:**
   - Null Hypothesis (H₀): There is no significant change in mood scores over the three weeks of yoga practice.
   - Alternate Hypothesis (H₁): There is a significant change in mood scores over the three weeks of yoga practice.

B. **Compute the F-ratio and Make a Decision Using α = 0.05:**
   - The F-ratio calculation involves comparing the variance between group means to the variance within the groups, using the given totals and sum of squares values. An α level of 0.05 indicates a 5% risk of concluding that a difference exists when there is none.

C. **Compute and Interpret the Effect Size for this Experiment:**
   - Effect size quantifies the magnitude of the difference irrespective of sample size. It helps in understanding the practical significance of the results beyond the p-values.

The calculations for B and C will require additional statistical techniques and context-specific assumptions.
Transcribed Image Text:**Mood Score Data from Yoga Class Study** In this study, volunteers participated in a yoga class three times per week for three weeks. Mood scores for three participants were collected weekly and are presented in the table below. | Subject | Week 1 | Week 2 | Week 3 | P-totals | |---------|--------|--------|--------|----------| | A | 3 | 4 | 5 | 12 | | B | 1 | 4 | 6 | 11 | | C | 2 | 1 | 6 | 9 | **Summary Statistics:** - For Subject B: - Total (T) = 15 - Sum of Squares (SS) = 2 - For Subject C: - Total (T) = 15 - Sum of Squares (SS) = 2 - Grand Total (G) = 27 - Sum of all squared scores (Σx²) = 108 **Analysis Tasks:** A. **State the Null and Alternate Hypotheses:** - Null Hypothesis (H₀): There is no significant change in mood scores over the three weeks of yoga practice. - Alternate Hypothesis (H₁): There is a significant change in mood scores over the three weeks of yoga practice. B. **Compute the F-ratio and Make a Decision Using α = 0.05:** - The F-ratio calculation involves comparing the variance between group means to the variance within the groups, using the given totals and sum of squares values. An α level of 0.05 indicates a 5% risk of concluding that a difference exists when there is none. C. **Compute and Interpret the Effect Size for this Experiment:** - Effect size quantifies the magnitude of the difference irrespective of sample size. It helps in understanding the practical significance of the results beyond the p-values. The calculations for B and C will require additional statistical techniques and context-specific assumptions.
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