Dr. Ferreira's research examines how intimate couples view their relationship. Dr. Ferreira asked each member of the couple to rate their happiness with the relationship and these data are below. Dr. Ferreira wants to know whether men or women have a more positive view of their relationship. What can Dr. Ferreira conclude? Show your work (Hypotheses, Statistical Test, Decision, & Conclusion). Data: Couple ID 1 2 3 4 5 6 7 8 9 10 Mean Standard Deviation Male 12 10 15 8 14 18 6. 9 7 14 11.3 3.92 Female 7 6. 11 11 15 4 7 6 3 7.8 3.61 Difference 3 -3 3 3 2 1 11 3.5 3.95 00 4.
Dr. Ferreira's research examines how intimate couples view their relationship. Dr. Ferreira asked each member of the couple to rate their happiness with the relationship and these data are below. Dr. Ferreira wants to know whether men or women have a more positive view of their relationship. What can Dr. Ferreira conclude? Show your work (Hypotheses, Statistical Test, Decision, & Conclusion). Data: Couple ID 1 2 3 4 5 6 7 8 9 10 Mean Standard Deviation Male 12 10 15 8 14 18 6. 9 7 14 11.3 3.92 Female 7 6. 11 11 15 4 7 6 3 7.8 3.61 Difference 3 -3 3 3 2 1 11 3.5 3.95 00 4.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
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Chapter1: Starting With Matlab
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Transcribed Image Text:**Title: Exploring Perceptions of Relationship Happiness Among Couples**
**Introduction:**
Dr. Ferreira's research focuses on understanding how intimate couples perceive their happiness within their relationships. Each partner was asked to rate their happiness, and the data collected aims to identify whether men or women have a more positive view of their relationship.
**Data Analysis:**
- **Hypotheses:**
- Null Hypothesis (H₀): There is no significant difference in relationship happiness ratings between men and women.
- Alternative Hypothesis (H₁): There is a significant difference in relationship happiness ratings between men and women.
- **Data Table:**
| Couple ID | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Mean | Standard Deviation |
|-----------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|------|-------------------|
| Male | 12 | 10 | 15 | 8 | 14 | 18 | 6 | 9 | 7 | 14 | 11.3 | 3.92 |
| Female | 8 | 7 | 6 | 11 | 11 | 15 | 4 | 7 | 6 | 3 | 7.8 | 3.61 |
| Difference| 4 | 3 | 9 | -3 | 3 | 3 | 2 | 2 | 1 | 11 | 3.5 | 3.95 |
**Explanation:**
The table above presents the happiness ratings provided by each couple’s male and female partners, along with their respective means and standard deviations. The difference row highlights the gap between male and female ratings for each couple.
**Conclusion:**
To determine the significance of the observed differences, a statistical test such as a paired t-test can be performed. Based on the calculations:
- **Decision:** If p-value < 0.05, reject the null hypothesis.
- **Conclusion:** If the null hypothesis is rejected, it suggests that there is a statistically significant difference in how men and women view their happiness within relationships.
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