Question

Doctors developed an intensive intervention program for obese patients with heart disease. a random sample of 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 lvef's are normally distributed. beforeafter 5859 4457 5362 5459 4960 4557 5765 4849 4356 4660 5661 for this problem, d = before - after, where the first data set represents "before" and the second data set represents "after". find the 95% confidence interval for the mean of the differences. round answers to 2 decimal places. < μ d

Answer 1

To find the 95% confidence interval for the mean difference in LVEF before and after intervention, we must calculate the mean difference, standard deviation, standard error, and then apply the t-distribution before rounding to two decimal places.

Step-by-step explanation:

To find the 95% confidence interval for the mean of the differences in the left ventricle ejection fraction (LVEF) before and after an intensive intervention program, we start by calculating the difference (d) for each patient using the formula d = before - after. Once we have these differences, we calculate the mean difference (d-bar), the standard deviation of the differences (SD), and the standard error of the mean (SEM). Finally, we use the t-distribution to find the confidence interval, taking into account the degrees of freedom (n-1).

1. 
   
3. Calculate the difference for each subject (before - after).
4. 
   
6. Calculate the mean of these differences.
7. 
   
9. Calculate the standard deviation of the differences.
10. 
    
12. Calculate the standard error of the mean (SEM = SD/√n).
13. 
    
15. Use the t-distribution to find the confidence interval: d-bar ± t*(SEM), where t* is the value from the t-distribution for n-1 degrees of freedom and a 95% confidence level.

After calculating the values, the final step is to round the confidence interval endpoints to two decimal places to present the findings.