, state the decision for the null hypothesis at a .05 level of significance. (Hint: Complete the table first.) a. there is not enough information to answer this question b. reject the null hypothesis c. fail to reject the null hypothesis

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Given the following one-way between-subjects ANOVA table, state the decision for the null hypothesis at a .05 level of significance. (Hint: Complete the table first.)

a. there is not enough information to answer this question
b. reject the null hypothesis
c. fail to reject the null hypothesis

 

### Analysis of Variance (ANOVA) Table

This table presents the results from an Analysis of Variance (ANOVA), a statistical method used to compare means across different groups and assess whether any of those means are statistically significantly different from each other.

| Source of Variation | SS  | *df* | *MS* | *F* |
|---------------------|-----|------|------|-----|
| **Between groups**  | 32  | 4    |      |     |
| **Within groups (error)** | 45  |      |      |     |
| **Total**           | 122 |      |      |     |

#### Explanation of Terms:

- **Source of Variation**: This column categorizes the variation into 'Between groups' and 'Within groups (error)'. 'Between groups' refers to the variability attributed to the differences between the group means, whereas 'Within groups (error)' refers to the variability within each group.

- **SS (Sum of Squares)**: This measures the total variability in the data. It is partitioned into 'Between groups' and 'Within groups'.

  - *Between groups*: 32
  - *Within groups*: 45
  - *Total*: 122

- **df (degrees of freedom)**: This indicates the number of independent values that can vary in the calculation of a statistic.

  - *Between groups*: 4

- **MS (Mean Square)**: This is the average of the sum of squares (SS) divided by its corresponding degrees of freedom (df). It is not filled in this table and usually calculated as SS/df.

- **F (F-ratio)**: This is a statistic used in ANOVA tests. It is a ratio of the variability between group means to the variability within the groups. This column is also not filled in this table.

The table segments the variation and evaluates the statistical significance of the group differences using the F-test, which helps in understanding whether the observed variations among group means are more than would be expected by chance alone.
Transcribed Image Text:### Analysis of Variance (ANOVA) Table This table presents the results from an Analysis of Variance (ANOVA), a statistical method used to compare means across different groups and assess whether any of those means are statistically significantly different from each other. | Source of Variation | SS | *df* | *MS* | *F* | |---------------------|-----|------|------|-----| | **Between groups** | 32 | 4 | | | | **Within groups (error)** | 45 | | | | | **Total** | 122 | | | | #### Explanation of Terms: - **Source of Variation**: This column categorizes the variation into 'Between groups' and 'Within groups (error)'. 'Between groups' refers to the variability attributed to the differences between the group means, whereas 'Within groups (error)' refers to the variability within each group. - **SS (Sum of Squares)**: This measures the total variability in the data. It is partitioned into 'Between groups' and 'Within groups'. - *Between groups*: 32 - *Within groups*: 45 - *Total*: 122 - **df (degrees of freedom)**: This indicates the number of independent values that can vary in the calculation of a statistic. - *Between groups*: 4 - **MS (Mean Square)**: This is the average of the sum of squares (SS) divided by its corresponding degrees of freedom (df). It is not filled in this table and usually calculated as SS/df. - **F (F-ratio)**: This is a statistic used in ANOVA tests. It is a ratio of the variability between group means to the variability within the groups. This column is also not filled in this table. The table segments the variation and evaluates the statistical significance of the group differences using the F-test, which helps in understanding whether the observed variations among group means are more than would be expected by chance alone.
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