Critical Thinking: Is the pain medicine Duragesic effective in reducing pain? Listed below are measures of pain intensity before and after using the drug Duragesic (fentanyl) (based on data from Janssen Pharmaceutical Products, L.P.). The data are listed in order by row, and corresponding measures are from the same subject before and after treatment. For example, the first subject had a measure of 1.2 before treatment and a measure of 0.4 after treatment. Each pair of measurements is from one subject, and the intensity of pain was measured using the standard visual analog score. A higher score corresponds to higher pain intensity.

Pain Intensity Before Duragesic Treatment

1.2	1.3	1.5	1.6	8	3.4	3.5	2.8	2.6	2.2
3	7.1	2.3	2.1	3.4	6.4	5	4.2	2.8	3.9
5.2	6.9	6.9	5	5.5	6	5.5	8.6	9.4	10
7.6

Pain Intensity After Duragesic Treatment

0.4	1.4	1.8	2.9	6	1.4	0.7	3.9	0.9	1.8
0.9	9.3	8	6.8	2.3	0.4	0.7	1.2	4.5	2
1.6	2	2	6.8	6.6	4.1	4.6	2.9	5.4	4.8
4.1

Two Independent Samples The methods of Section 9-2 can be used to test the claim that two populations have the same mean. Identify the specific claim that the treatment is effective, then use the methods of Section 9-2 to test that claim. The methods of Section 9-2 are based on the requirement that the samples are independent. Are they independent in this case?

The pain intensities of a group of subjects are recorded before and after using the drug Duragesic.

It is given that the drug Duragesic is administered to a group of subjects to see if the drug is effective in reducing pain.

Thus, an appropriate claim would be that the drug Duargesic is effective in reducing pain.

Corresponding to the given claim, the following hypotheses are noted:

Null Hypothesis: The mean value of the pain intensity before the treatment is equal to the mean value of the pain intensity after the treatment.

\({H_0}:{\mu _1} = {\mu _2}\)

Alternative Hypothesis: The mean value of the pain intensity before the treatment is greater than the mean value of the pain intensity after the treatment.

\({H_1}:{\mu _1} > {\mu _2}\)

The method discussed in Section 9-2 deals with testing the claim for the two population means.

The method requires the given samples to be independent.

Two samples are said to be independent if the sample units taken from one population are not the same (matched) as the sample units taken from the other population.

Here, the same set of subjects were used as sample units for both the samples; once before administering the drug and then after administering the drug.

Thus, the samples have matched pairs.

Since one of the requirements is not fulfilled, the given two samples cannot be used to test the stated claim using the methods of Section 9-2.