MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Dr. Phil wanted to know if mothers give more hugs to their children than fathers do. He used 8 married couples so that each mother and father would be matched on the number of children for his sample. Dr. Phil then asked each parent to report the number of hugs that they gave their children over the course of 2 weeks. Assume the parametric assumptions were NOT violated. Conduct an appropriate statistical test for him using alpha .05 and the eight steps of hypothesis testing.
Note: more information given in table than is needed
Transcribed Image Text:The image contains a table used for statistical analysis in an educational setting. Dr. Phil conducted a study to determine if mothers give more hugs to their children than fathers do. The study involved 8 married couples, matching each mother and father based on the number of their children. Participants were asked to report the number of hugs given to their children over two weeks.
### Table Details:
The table includes the following columns:
1. **Pair**: Identifies each couple by a number from 1 to 8.
2. **Mother Hugs (X1)**: Number of hugs given by mothers.
3. **R1**: Square of the mother hugs (X1²).
4. **Father Hugs (X2)**: Number of hugs given by fathers.
5. **R2**: Square of the father hugs (X2²).
6. **D**: Difference between mother and father hugs (X1 - X2).
7. **Ranks**: Rank assigned based on the absolute difference.
8. **D²**: Square of the difference.
9. **+**: Additional information.
### Data Summary:
- **Mother Hugs (X1)**: Total of 73
- **Father Hugs (X2)**: Total of 91
- **Sum of Differences (D)**: -18
- **Sum of Squared Differences (D²)**: 100
- **Mean Hugs**:
- Mothers: 9.125
- Fathers: 11.375
- Mean Difference: -2.25
This setup is used to conduct a statistical hypothesis test using a significance level of α = 0.05. The instructions indicate the need to follow eight steps of hypothesis testing, typically including steps like stating hypotheses, selecting a significance level, and interpreting the results.
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