A cognitive psychologist studying motivation wants to determine if type of music has any effect on the number of days (in 1 month) participants visit a gym. A total of four gyms are selected that have different musical formats. 8 gym members are randomly sampled from each gym, and their gym attendance is monitored for 30 days. Complete the following ANOVA summary table, and use a significance level of α = 0.02. Source Between Within TOTAL SS df MS 13.64 F 2.788 P

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**Study Overview:**

A cognitive psychologist is investigating whether the type of music played at gyms affects the number of days participants attend the gym over a month. Four different gyms, each with a unique musical format, are selected for this study. Eight gym members are randomly chosen from each gym, and their attendance is tracked for 30 days.

**ANOVA Summary Table:**

The table below outlines the Analysis of Variance (ANOVA) used to analyze the data. The significance level is set at \(\alpha = 0.02\).

| Source   | SS  | df | MS   | F     | P  |
|----------|-----|----|------|-------|----|
| Between  |     |    | 13.64| 2.788 |    |
| Within   |     |    |      |       |    |
| TOTAL    |     |    |      |       |    |

**Explanation of Table Columns:**

- **Source:** Identifies the source of variance (Between and Within groups are typically analyzed).
- **SS (Sum of Squares):** Represents the variability in the data.
- **df (Degrees of Freedom):** Details the number of values that can vary for each source of variance.
- **MS (Mean Square):** Calculated by dividing SS by df for each source, indicating the average variance.
- **F (F-ratio):** A statistic used to determine if the means between groups are significantly different.
- **P:** The p-value, used to decide whether to reject the null hypothesis at a specific significance level. 

The table is currently incomplete and requires additional data for SS, df, and potentially P. This information will reveal whether music type significantly affects gym attendance.
Transcribed Image Text:**Study Overview:** A cognitive psychologist is investigating whether the type of music played at gyms affects the number of days participants attend the gym over a month. Four different gyms, each with a unique musical format, are selected for this study. Eight gym members are randomly chosen from each gym, and their attendance is tracked for 30 days. **ANOVA Summary Table:** The table below outlines the Analysis of Variance (ANOVA) used to analyze the data. The significance level is set at \(\alpha = 0.02\). | Source | SS | df | MS | F | P | |----------|-----|----|------|-------|----| | Between | | | 13.64| 2.788 | | | Within | | | | | | | TOTAL | | | | | | **Explanation of Table Columns:** - **Source:** Identifies the source of variance (Between and Within groups are typically analyzed). - **SS (Sum of Squares):** Represents the variability in the data. - **df (Degrees of Freedom):** Details the number of values that can vary for each source of variance. - **MS (Mean Square):** Calculated by dividing SS by df for each source, indicating the average variance. - **F (F-ratio):** A statistic used to determine if the means between groups are significantly different. - **P:** The p-value, used to decide whether to reject the null hypothesis at a specific significance level. The table is currently incomplete and requires additional data for SS, df, and potentially P. This information will reveal whether music type significantly affects gym attendance.
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