Questions: Researchers wish to design a matched pairs experiment to determine the effects of a medication on reducing LDL cholesterol levels in 400 adults in the 65 and older age group who have elevated levels of LDL. Which of the following represents such a design? (A) They compare the cholesterol levels of each patient before he/she begins a daily regimen of the medicine to the patient's cholesterol level after taking the medicine. (C) They compare the mean cholesterol level for all adults who are 65 and older who take the medicine for six weeks with the published national mean cholesterol levels of adults in the 65 and older age group who were taking a placebo. (D) They compare the cholesterol levels of 400 adults in the 65 and older age group before and after taking the medicine.

Researchers wish to design a matched pairs experiment to determine the effects of a medication on reducing LDL cholesterol levels in 400 adults in the 65 and older age group who have elevated levels of LDL. Which of the following represents such a design?
(A) They compare the cholesterol levels of each patient before he/she begins a daily regimen of the medicine to the patient's cholesterol level after taking the medicine.
(C) They compare the mean cholesterol level for all adults who are 65 and older who take the medicine for six weeks with the published national mean cholesterol levels of adults in the 65 and older age group who were taking a placebo.
(D) They compare the cholesterol levels of 400 adults in the 65 and older age group before and after taking the medicine.

Transcript text: Researchers wish to design a matched pairs experiment to determine the effects of a medication on reducing LDL cholesterol levels in 400 adults in the 65 and older age group who have elevated levels of LDL. Which of the following represents such a design? (A) They compare the cholesterol levels of each patient before he/she begins a daily regimen of the medicine to the patient's cholesterol level after taking the medicine. (C) They compare the mean cholesterol level for all adults who are 65 and older who take the medicine for six weeks with the published national mean cholesterol levels of adults in the 65 and older age group who were taking a placebo. (D) They compare the cholesterol levels of 400 adults in the 65 and older age group before and after taking the medicine.

Solution

Solution Steps

Solution Approach

To design a matched pairs experiment, each participant's cholesterol level should be measured before and after taking the medication. This allows for a direct comparison of the effect of the medication on each individual, controlling for individual variability.

Step 1: Data Collection

The cholesterol levels of five participants were recorded before and after taking the medication. The values are as follows:

Before medication: \( [200, 220, 210, 230, 240] \)
After medication: \( [180, 200, 190, 210, 220] \)

Step 2: Calculate Differences

The differences in cholesterol levels for each participant were calculated as follows: \[ \text{differences} = [200 - 180, 220 - 200, 210 - 190, 230 - 210, 240 - 220] = [20, 20, 20, 20, 20] \]

Step 3: Average Difference

The average difference in cholesterol levels after medication is computed: \[ \text{average difference} = \frac{20 + 20 + 20 + 20 + 20}{5} = \frac{100}{5} = 20.0 \]