4. 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 iş needed Mother Hugs R1 Father Hugs (X2) Pair (X1) X12 R2 X22 Ranks D2 1 14 196 14 196 10 100 64 2 14 3 10 100 15 225 -5 25 4 8. 64 49 36 81 -3 19 6 3 81 -6 36 7 17 289 20 400 25 9 81 16 Total 73 819 91 1177 -18 100 Means 9.125 11.375 -2.25

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### Study Overview

Dr. Phil aimed to investigate whether mothers give more hugs to their children than fathers do. He conducted a study with 8 married couples, where each parent was tasked with recording the number of hugs given to their children over a two-week period. The study ensures that parametric assumptions were not violated.

### Research Objective

The primary objective is to determine if there is a statistically significant difference between the number of hugs given by mothers versus fathers, using an alpha level of 0.05 and the eight steps of hypothesis testing.

### Data Table

The data collected is presented in a table with the following columns:

- **Pair**: Represents the couple number from 1 to 8.
- **Mother Hugs (X1)**: Number of hugs given by mothers.
- **R1**: Squared value of Mother Hugs (X1).
- **X1²**: Calculated value (X1 squared).
- **Father Hugs (X2)**: Number of hugs given by fathers.
- **R2**: Squared value of Father Hugs (X2).
- **X2²**: Calculated value (X2 squared).
- **D**: Difference between Mother Hugs and Father Hugs (X1 - X2).
- **Ranks**: Ranking of differences.
- **D²**: Squared differences.
- **+/-**, blank column for sign indication.

### Detailed Data Points

- **Pair 1**: 
  - Mother Hugs: 14, Father Hugs: 14
  - Difference (D): 0, Squared Difference (D²): 0

- **Pair 2**: 
  - Mother Hugs: 10, Father Hugs: 8
  - Difference (D): 2, Squared Difference (D²): 4

- **Pair 3**: 
  - Mother Hugs: 10, Father Hugs: 15
  - Difference (D): -5, Squared Difference (D²): 25

- **Pair 4**: 
  - Mother Hugs: 8, Father Hugs: 7
  - Difference (D): 1, Squared Difference (D²): 1

- **Pair 5**: 
  - Mother Hugs: 6, Father Hugs: 9
  - Difference (D): -3
Transcribed Image Text:### Study Overview Dr. Phil aimed to investigate whether mothers give more hugs to their children than fathers do. He conducted a study with 8 married couples, where each parent was tasked with recording the number of hugs given to their children over a two-week period. The study ensures that parametric assumptions were not violated. ### Research Objective The primary objective is to determine if there is a statistically significant difference between the number of hugs given by mothers versus fathers, using an alpha level of 0.05 and the eight steps of hypothesis testing. ### Data Table The data collected is presented in a table with the following columns: - **Pair**: Represents the couple number from 1 to 8. - **Mother Hugs (X1)**: Number of hugs given by mothers. - **R1**: Squared value of Mother Hugs (X1). - **X1²**: Calculated value (X1 squared). - **Father Hugs (X2)**: Number of hugs given by fathers. - **R2**: Squared value of Father Hugs (X2). - **X2²**: Calculated value (X2 squared). - **D**: Difference between Mother Hugs and Father Hugs (X1 - X2). - **Ranks**: Ranking of differences. - **D²**: Squared differences. - **+/-**, blank column for sign indication. ### Detailed Data Points - **Pair 1**: - Mother Hugs: 14, Father Hugs: 14 - Difference (D): 0, Squared Difference (D²): 0 - **Pair 2**: - Mother Hugs: 10, Father Hugs: 8 - Difference (D): 2, Squared Difference (D²): 4 - **Pair 3**: - Mother Hugs: 10, Father Hugs: 15 - Difference (D): -5, Squared Difference (D²): 25 - **Pair 4**: - Mother Hugs: 8, Father Hugs: 7 - Difference (D): 1, Squared Difference (D²): 1 - **Pair 5**: - Mother Hugs: 6, Father Hugs: 9 - Difference (D): -3
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