Question

A new drug to lower total cholesterol is being tested. A study is designed to evaluate the efficacy of the drug. Sixteen patients agree to participate in the study and each is asked to take the new drug for 4 weeks. Before starting the treatment, each patient's total cholesterol level is measured. After taking the drug for 4 weeks, each patient's total cholesterol level is measured again. The 99% confidence interval for the change in total cholesterol (After less Before) is computed to be (-12.8245 mg/dl, 0.0455mg/dl).

1. Provide an interpretation of the 99% confidence interval for the population mean difference in total cholesterol levels associated with taking the new drug for 4 weeks. Select all correct interpretations.

A. We prove that the population mean difference in total cholesterol levels (After less Before) for the population of all patients who took or will take the new drug for 4 weeks is -6.3895 mg/dl with the 99% margin of error of 6.435 mg/dl.
B. With 99% confidence, we estimate that the population mean difference in total cholesterol levels (After less Before) for the population of all patients who took or will take the new drug for 4 weeks is between -12.8245 mg/dl and 0.0455 mg/dl.
C. If this study was repeated many times, then we would expect 99% of the resulting 99% confidence intervals to contain the population mean difference in total cholesterol levels for the population of all patients who took or will take the new drug for 4 weeks.
D. We estimate that the population mean difference in total cholesterol levels (After less Before) for the population of all patients who took or will take the new drug for 4 weeks is -6.3895 mg/dl with the 99% margin of error of 6.435 mg/dl.
E. With 99% confidence, we estimate that the sample mean difference in total cholesterol levels (After less Before) for the population of all patients who took or will take the new drug for 4 weeks is between -12.8245 mg/dl and 0.0455 mg/dl.
F. With 99% confidence, we demonstrate that the population mean difference in total cholesterol levels (After less Before) for the population of all patients who took or will take the new drug for 4 weeks is between -12.8245 mg/dl and 0.0455 mg/dl.
G. With 99% confidence, we estimate that in the population of all patients who took or will take the new drug, the total cholesterol level for each patient after taking the new drug for 4 weeks will be is between -12.8245 mg/dl lower and 0.0455 mg/dl higher than before taking the drug, on average.
H. With 99% confidence, we estimate that the population mean difference in total cholesterol levels (Before less After) for the population of all patients who took or will take the new drug for 4 weeks is between -0.0455 mg/dl and 12.8245 mg/dl.

Answer 1