Question

value: 3
a randomized comparative experiment tests whether a cholesterol medication lowers the overall blood pressure for male patients. the control group has ten male patients and the treatment group, which receives the medication, has 10 male patients. all patients started with cholesterol level of 245 mg/dl.

	cholesterol in mg/dl
treatment	230	225	220	218	224	240	232	221	235	224

did the cholesterol medication lower the cholesterol levels?
a. yes. the treatment group had a lower level of cholesterol overall.
b. yes. the control group had a lower level of cholesterol overall.
c. no. the treatment group had a higher level of cholesterol overall.
d. no. the treatment group had the same level of cholesterol overall.

Explanation:

Step1: Calculate the average cholesterol level of the control group

Let the cholesterol - level values of the control group be \(x_1,x_2,\cdots,x_{10}\). The sum of the cholesterol - level values in the control group \(S_{c}=\sum_{i = 1}^{10}x_i=241 + 243+242+245+250+248+246+245+242+247 = 2459\). The average cholesterol level of the control group \(\bar{x}_{c}=\frac{S_{c}}{10}=\frac{2459}{10}=245.9\) mg/dL.

Step2: Calculate the average cholesterol level of the treatment group

Let the cholesterol - level values of the treatment group be \(y_1,y_2,\cdots,y_{10}\). The sum of the cholesterol - level values in the treatment group \(S_{t}=\sum_{i = 1}^{10}y_i=230 + 225+220+218+224+240+232+221+235+224 = 2269\). The average cholesterol level of the treatment group \(\bar{x}_{t}=\frac{S_{t}}{10}=\frac{2269}{10}=226.9\) mg/dL.

Step3: Compare the average cholesterol levels

Since \(\bar{x}_{t}=226.9\) mg/dL and \(\bar{x}_{c}=245.9\) mg/dL, and \(226.9<245.9\), the treatment group had a lower level of cholesterol overall.

Answer:

A. Yes. The treatment group had a lower level of cholesterol overall