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 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: -2.25This 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.

Given information: Pair Mother Hugs Father Hugs 1 14 14 2 10 8 3 10 15 4 8 7 5 6 9 6 3 9 7 17 20 8 5 9 Null hypothesis: H0: μDifference=0 Alternate hypothesis: HA: μDifference>0 This is one tailed test. The significance level is 0.05 and we will conduct a matched-pairs t-test of the null hypothesis. Use the given data to form the excel table: Pair Mother Hugs Father Hugs d d-d¯2 1 14 14 0 5.0625 2 10 8 2 18.0625 3 10 15 -5 7.5625 4 8 7 1 10.5625 5 6 9 -3 0.5625 6 3 9 -6 14.0625 7 17 20 -3 0.5625 8 5 9 -4 3.0625 Sum 73 91 -18 59.5 Mean 9.125 11.375 -2.25 7.4375 Use the sample data to calculate the standard deviation of the differences(s), the standard error (S.E) of the mean difference, the degrees of freedom(DF), and the t statistic test statistic(t). s=∑(d-d¯)2n-1=59.58-1s=2.915475947≈2.9155S.E=sn=2.91558=1.0307764≈1.0308D.F=n-1=8-1=7 t=[(x1-x2)-D]S.E=-2.25-01.0308=-2.182820625≈-2.18 The P-value for this test is the probability that a t statistic having 7 degrees of freedom is greater than - 2.18. P-value = P(t >-2.18) Use the excel formula, "=T.DIST.RT(-2.18,7)" to determine the P-value. P-value = 0.9672 Decision: Since the P-value (0.9672) is greater than the significance level (0.05), hence we failed to reject the null hypothesis. Conclusion: From the above test we do not have sufficient evidence in the favor of the claim that mothers give more hugs to their children than fathers do.