Doctors developed an intensive intervention program for obese patients with heart disease. Subjects with a BMI of 30 kg/m² or more, with heart disease, were assigned to a three-month lifestyle change of diet and exercise. Patients’ Left Ventricle Ejection Fraction (LVEF) are measured before and after intervention. A normal heart’s ejection fraction may be between 50 and 70 percent; higher numbers indicate a healthier heart. Assume LVEFs are normally distributed.| Before | After ||--------|-------|| 45 | 56 || 52 | 60 || 53 | 63 || 47 | 59 || 42 | 57 || 51 | 57 || 54 | 57 || 46 | 55 || 57 | 67 || 53 | 62 || 48 | 59 || 53 | 63 || 51 | 61 || 38 | 51 |Find the 90% confidence interval for the mean of the differences. Use technology to find the critical value and round answers to at least 4 decimal places.Did the intensive intervention program significantly increase the LVEF measurements? [Yes/No]

Compute the difference in each pair of observations by subtracting the observation in the "Before" column from the respective observations in the "After" column. Before After Difference (d) 45 56 11 52 60 8 53 63 10 42 59 17 47 57 10 56 67 11 45 55 10 62 67 5 54 57 3 47 57 10 41 50 9 53 63 10 53 58 5 49 61 12 53 61 8 35 56 21 38 51 13 Compute the mean of the difference series using the formula: d¯=∑idin d¯=11+8+10+,...,+1317 =17317 =10.1765Compute the standard deviation of the difference series using the formula: sd=∑idi-d¯2n-1 sd=11-10.17652+8-10.17652+10-10.17652+,...,+13-10.1765217-1 =0.6782+4.7370+0.0311+,...,+7.972316 =292.470616 =18.2794 =4.2754Compute the level of significance using the formula: α=1-confidence level α=1-0.90 =0.10 Compute the degrees of freedom using the formula: df=n-1 df=17-1 =16 By using the technology, the critical value tα2 for the 16 degrees of freedom and at the 0.10 level of significance is 1.7459. Compute the 90% confidence interval for the mean of the differences using the formula: d¯-tα2sdn<μd<d¯+tα2sdn 10.1765-1.74594.275417<μd<10.1765+1.74594.27541710.1765-1.8104<μd<10.1765+1.81048.3661<μd<11.9869 Because the differences are calculated by subtracting the Before data from the After data, and the interval comprises all positive values, the intensive intervention program greatly improves the LVEF measures. Furthermore, the interval does not include 0, implying that the difference is significant.