Question

(1 point) 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. 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.

B. 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.

C. 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.

D. 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.

E. 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.

F. 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.

G. 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.

H. 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.

2. Interpret the 99% confidence level for the population mean difference in total cholesterol levels associated with taking the new drug for 4 weeks. Select all correct interpretations.

A. If this study was repeated many times, then we would expect 99% of the patients to have their total cholesterol level reduced by 99% for the population of all patients who took or will take the new drug for 4 weeks.

B. The percentage of patients in this study whose total cholesterol level reduced by between -12.8245 mg/dl and 0.0455 mg/dl after taking the new drug for 4 weeks, is 99%.

C. 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.

D. 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.

E. The probability 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 is 99%.

F. If this study was repeated many times, then we would expect 99% of the resulting 99% confidence intervals to contain the sample mean difference in total cholesterol levels for the population of all patients who took or will take the new drug for 4 weeks

Answer 1

The 99% confidence interval for the change in total cholesterol (After less Before) is computed to be (-12.8245 mg/dl, 0.0455mg/dl).

A 99% confidence interval is a range of values that you can be 99% certain contains the true population mean difference in total cholesterol (After less Before). Hence

1) option A is right

2) option c is right