### Study OverviewDr. 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 ObjectiveThe 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 TableThe 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

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.