Ho:H1:Cv:Tv:What is the Decision? ### One-Way ANOVA Test**Scenario:** Three sports teams took a random sample of GPAs for the last year. Use alpha (α) = 0.1 to determine if the means are all equal.#### Data:| Track | Basketball | Soccer ||-------|-------------|-------|| 3.6 | 3.5 | 4.0 || 2.9 | 3.9 | 2.0 || 2.5 | 3.1 | 3.2 || 3.3 | 3.4 | 3.2 |### Explanation of the Data:The table above provides the GPAs for students from Track, Basketball, and Soccer teams. Each column represents the GPAs for a team, and each row corresponds to an individual student's GPA from that team.#### Procedure:1. **State the Hypotheses:** - Null Hypothesis (H0): The means of the GPAs for all three sports teams are equal. - Alternative Hypothesis (H1): At least one of the means is different.2. **Level of Significance:** - Use alpha (α) = 0.13. **Calculate the ANOVA:** - Compute the grand mean of all observations. - Calculate the Between-Group Variability (SSB). - Calculate the Within-Group Variability (SSW). - Compute the F-statistic using the formula: \[ F = \frac{\text{MSB}}{\text{MSW}} \] where, - MSB = SSB / (k - 1) - MSW = SSW / (N - k) Here, $k$ is the number of groups, and $N$ is the total number of observations.4. **Decision Rule:** - Compare the calculated F-statistic with the critical value from F-distribution tables for (df1, df2) degrees of freedom, where $df1 = k-1$ and $df2 = N - k$.5. **Conclusion:** - If F-calculated > F-critical, reject the null hypothesis. Otherwise, do not reject the null hypothesis.### Interpretation:This ANOVA test will help you understand if there is a significant difference

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Description: Ho:H1:Cv:Tv:What is the Decision? ### One-Way ANOVA Test**Scenario:** Three sports teams took a random sample of GPAs for the last year. Use alpha (α) = 0.1 to determine if the means are all equal.#### Data:| Track | Basketball | Soccer ||-------|---

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Three sports teams took a random sample of GPAS for the last year. Use alpha = 0.1 to determine if the means are all equal. Track 3.6 Basketball Soccer 3.5 4 2.9 3.9 2.0 2.5 3.1 3.2 3.3 3.4 3.2

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Ho:

H1:

Cv:

Tv:

What is the Decision?

### One-Way ANOVA Test

**Scenario:**
Three sports teams took a random sample of GPAs for the last year. Use alpha (α) = 0.1 to determine if the means are all equal.

#### Data:

| Track | Basketball | Soccer |
|-------|-------------|-------|
| 3.6 | 3.5 | 4.0 |
| 2.9 | 3.9 | 2.0 |
| 2.5 | 3.1 | 3.2 |
| 3.3 | 3.4 | 3.2 |

### Explanation of the Data:

The table above provides the GPAs for students from Track, Basketball, and Soccer teams. Each column represents the GPAs for a team, and each row corresponds to an individual student's GPA from that team.

#### Procedure:
1. **State the Hypotheses:**
- Null Hypothesis (H0): The means of the GPAs for all three sports teams are equal.
- Alternative Hypothesis (H1): At least one of the means is different.

2. **Level of Significance:**
- Use alpha (α) = 0.1

3. **Calculate the ANOVA:**
- Compute the grand mean of all observations.
- Calculate the Between-Group Variability (SSB).
- Calculate the Within-Group Variability (SSW).
- Compute the F-statistic using the formula:

\[
F = \frac{\text{MSB}}{\text{MSW}}
\]

where,
- MSB = SSB / (k - 1)
- MSW = SSW / (N - k)

Here, $k$ is the number of groups, and $N$ is the total number of observations.

4. **Decision Rule:**
- Compare the calculated F-statistic with the critical value from F-distribution tables for (df1, df2) degrees of freedom, where $df1 = k-1$ and $df2 = N - k$.

5. **Conclusion:**
- If F-calculated > F-critical, reject the null hypothesis. Otherwise, do not reject the null hypothesis.

### Interpretation:
This ANOVA test will help you understand if there is a significant difference

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