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 4 10 Mean Standard Deviation Male 12 10 15 14 18 6. 7. 11.3 3.92 Female 8 7. 11 11 15 4. 7. 3 7.8 3.61 Difference 4 3. -3 3 11 3.5 3.95 14 8 2. 7. 6. 3. 90 2.

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**Research Overview:**

Dr. Ferreira's study explores how intimate couples perceive their relationship. Each partner rated their happiness within the relationship, and the data collected is summarized below. The aim is to determine if there is a significant difference in relationship happiness between men and women. 

**Data Analysis:**

A table with happiness ratings for both male and female partners in couples is presented. 

- **Ratings:**

  - **Couple ID:** 1 to 10

  - **Male Ratings:** 12, 10, 15, 8, 14, 18, 6, 9, 7, 14

  - **Female Ratings:** 8, 7, 6, 11, 11, 15, 4, 7, 6, 3

  - **Difference (Male - Female):** 4, 3, 9, -3, 3, 3, 2, 2, 1, 11

- **Statistical Summary:**

  - **Mean Ratings:**
    - Male: 11.3
    - Female: 7.8
    - Difference: 3.5

  - **Standard Deviation:**
    - Male: 3.92
    - Female: 3.61
    - Difference: 3.95

**Interpretation:**

Dr. Ferreira should conduct a hypothesis test to evaluate if the observed differences in mean happiness ratings are statistically significant. This involves stating the null and alternative hypotheses, choosing an appropriate statistical test, making a decision based on the test results, and drawing a conclusion on whether men or women have a more positive view of their relationship.
Transcribed Image Text:**Research Overview:** Dr. Ferreira's study explores how intimate couples perceive their relationship. Each partner rated their happiness within the relationship, and the data collected is summarized below. The aim is to determine if there is a significant difference in relationship happiness between men and women. **Data Analysis:** A table with happiness ratings for both male and female partners in couples is presented. - **Ratings:** - **Couple ID:** 1 to 10 - **Male Ratings:** 12, 10, 15, 8, 14, 18, 6, 9, 7, 14 - **Female Ratings:** 8, 7, 6, 11, 11, 15, 4, 7, 6, 3 - **Difference (Male - Female):** 4, 3, 9, -3, 3, 3, 2, 2, 1, 11 - **Statistical Summary:** - **Mean Ratings:** - Male: 11.3 - Female: 7.8 - Difference: 3.5 - **Standard Deviation:** - Male: 3.92 - Female: 3.61 - Difference: 3.95 **Interpretation:** Dr. Ferreira should conduct a hypothesis test to evaluate if the observed differences in mean happiness ratings are statistically significant. This involves stating the null and alternative hypotheses, choosing an appropriate statistical test, making a decision based on the test results, and drawing a conclusion on whether men or women have a more positive view of their relationship.
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