Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Textbook Question
Chapter 11.3, Problem 8AYU
Sugary Beverages It has been reported that consumption of sodas and other sugar-sweetened beverages cause excessive weight gain. Researchers conducted a randomized study in which 224 overweight and obese adolescents who regularly consumed sugar-sweetened beverages were randomly assigned to experimental and control groups. The experimental groups received a one-year intervention designed to decrease consumption of sugar-sweetened beverages, with follow-up for an additional year without intervention. The response variable in the study was body mass index (BMI—the weight in kilograms divided by the square of the height in meters). Results of the study appear in the following table.
Source: Cara B. Ebbeling, PhD and associates, “A Randomized Trial of Sugar-Sweetened Beverages and Adolescent Body Weight.” N Engl J Med 2012:357:1407–16. DOI: 10.1056/NEJMoal2Q3388
| Experimental Group (n = 110) | Control Group (n = 114) | |
| Start of Study | Standard Deviation BMI = 5.2 |
Mean BMI = 30.1 Standard Deviation BMI = 4.7 |
| After One Year | Mean Change in BMI = 0.06 Standard Deviation Change in BMI = 0.20 |
Mean Change in BMI = 0.63 Standard Deviation Change in BMI = 0.20 |
| After Two Years | Mean Change in BMI = 0.71 Standard Deviation Change in BMI = 0.28 |
Mean Change in BMI = 1.00 Standard Deviation Change in BMI = 0.28 |
- a. What type of experimental design is this?
- b. What is the response variable? What is the explanatory variable?
- c. One aspect of statistical studies is to verify that the subjects in the various treatment groups are similar. Does the sample evidence support the belief that the BMIs of the subjects in the experimental group is not different from the BMIs in the control group at the start of the study? Use an α = 0.05 level of significance.
- d. One goal of the research was to determine if the change in BMI for the experimental group was less than that for the control group after one year. Conduct the appropriate test to see if the evidence suggests this goal was met. Use an α = 0.05 level of significance. What does this result suggest?
- e. Does the sample evidence suggest the change in BMI is less for the experimental group than the control group after two years? Use an α = 0.05 level of significance. What does this result suggest?
- f. To what population do the results of this study apply?
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Chapter 11 Solutions
Fundamentals of Statistics (5th Edition)
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