A psychologist would like to know whether the season (autumn, winter, spring, and summer) has any consistent effect on people's sexual activity. In the middle of each season, a psychologist selects a random sample of 23 students. Each individual is given a sexual activity questionnaire. A one-factor ANOVA was used to analyze these data. Complete the following ANOVA summary table (a = 0.05). Round your answers to three decimal places, if necessary. Hint: Find the MSB, and work backwards, using the dfB. Hint: What is the relationship between SSB, SSW, and SST? df Source Between Within Total SS 58.59 X 473.44 532.03 X 3 ✓ 88 91 MS 19.53 5.38 F P-value 3.63 0.0160
A psychologist would like to know whether the season (autumn, winter, spring, and summer) has any consistent effect on people's sexual activity. In the middle of each season, a psychologist selects a random sample of 23 students. Each individual is given a sexual activity questionnaire. A one-factor ANOVA was used to analyze these data. Complete the following ANOVA summary table (a = 0.05). Round your answers to three decimal places, if necessary. Hint: Find the MSB, and work backwards, using the dfB. Hint: What is the relationship between SSB, SSW, and SST? df Source Between Within Total SS 58.59 X 473.44 532.03 X 3 ✓ 88 91 MS 19.53 5.38 F P-value 3.63 0.0160
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
Transcribed Image Text:## Analysis of Sexual Activity Across Seasons Using ANOVA
A psychologist aims to determine if the season (autumn, winter, spring, and summer) consistently affects people's sexual activity. In the middle of each season, a random sample of 23 students is surveyed using a sexual activity questionnaire. A one-factor ANOVA evaluates the collected data. Answers should be rounded to three decimal places.
### ANOVA Summary Table
| Source | SS | df | MS | F | P-value |
|---------|--------|-----|-------|------|---------|
| Between | 58.59 | 3 | 19.53 | 3.63 | 0.0160 |
| Within | 473.44 | 88 | 5.38 | | |
| Total | 532.03 | 91 | | | |
**Hints:**
- To find \( MS_B \) (Mean Square Between), work backwards using the \( df_B \) (degrees of freedom between).
- Understand the relationship between \( SS_B \) (Sum of Squares Between), \( SS_W \) (Sum of Squares Within), and \( SS_T \) (Total Sum of Squares).
### Explanation
- **Between Groups (Between)**: This represents the variance due to the interaction between the groups—seasonal effects in this case.
- **Within Groups (Within)**: Accounts for variance within each group.
- **Degrees of Freedom (df)**: Indicates the number of independent values that can vary in the analysis.
- For Between Groups: \( df_B = 3 \)
- For Within Groups: \( df_W = 88 \)
- Total \( df_T = 91 \)
- **Mean Square (MS)**: SS divided by its respective df.
- **F-value**: Calculated by dividing the MS between by MS within; used to determine statistical significance.
- **P-value**: Shows the probability that the observed results occurred by chance. A P-value less than 0.05 indicates statistical significance.
This table indicates a statistically significant effect of the seasons on sexual activity, as shown by a P-value of 0.0160.
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