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Chapter 10: Q3FDD (page 468)

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?

Short Answer

Expert verified

The claim that needs to be tested is thatthe drug Duargesic is effective in reducing pain.

Since the samples are not independent, the stated claim cannot be tested using the methods of Section 9-2.

Step by step solution

01

Given information

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

02

Claim to be tested

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.

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

03

Method of hypothesis testing

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.

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Most popular questions from this chapter

Testing for a Linear Correlation. In Exercises 13鈥�28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

Old Faithful Listed below are duration times (seconds) and time intervals (min) to the next eruption for randomly selected eruptions of the Old Faithful geyser in Yellowstone National Park. Is there sufficient evidence to conclude that there is a linear correlation between duration times and interval after times?

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251

262

207

140

Interval After

91

81

91

92

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Cell Phones and Driving In the author鈥檚 home town of Madison, CT, there were 2733 police traffic stops in a recent year, and 7% of them were attributable to improper use of cell phones. Use a 0.05 significance level to test the claim that the sample is from a population in which fewer than 10% of police traffic stops are attributable to improper cell phone use.

Outlier Refer to the accompanying Minitab-generated scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a correlation between x and y. b. After identifying the 10 pairs of coordinates corresponding to the 10 points, find the value of the correlation coefficient r and determine whether there is a linear correlation. c. Now remove the point with coordinates (10, 10) and repeat parts (a) and (b). d. What do you conclude about the possible effect from a single pair of values?

let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10-5 on page 493. Use a 0.05 significance level.

For 30 recent Academy Award ceremonies, ages of Best Supporting Actors (x) and ages of Best Supporting Actresses (y) are recorded. The 30 paired ages yield\(\bar x = 52.1\)years,\(\bar y = 37.3\)years, r= 0.076, P-value = 0.691, and

\(\hat y = 34.4 + 0.0547x\). Find the best predicted value of\(\hat y\)(age of Best Supporting Actress) in 1982, when the age of the Best Supporting Actor (x) was 46 years.

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










Matched Pairs The methods of Section 9-3 can be used to test a claim about matched data. Identify the specific claim that the treatment is effective, then use the methods of Section 9-3 to test that claim.
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