91Ó°ÊÓ

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, \(\mathrm{PhD}\) and associates, "A Randomized Trial of Sugar-Sweetened Beverages and Adolescent Body Weight" N Engl J Med 2012;367:1407-16. DOI: 10.1056/NEJMoal2Q3388 $$ \begin{array}{lll} & \text { Experimental } & \text { Control } \\ & \text { Group } & \text { Group } \\ & (n=110) & (n=114) \\ \hline \text { Start of Study } & \text { Mean BMI }=30.4 & \text { Mean BMI }=30.1 \\ & \text { Standard Deviation } & \text { Standard Deviation } \\ & \mathrm{BMI}=5.2 & \mathrm{BMI}=4.7 \\ \hline \text { After One Year } & \text { Mean Change in } & \text { Mean Change in } \\ & \mathrm{BMI}=0.06 & \mathrm{BMI}=0.63 \\ & \text { Standard Deviation } & \text { Standard Deviation } \\ & \text { Change in } & \text { Change in } \\ & \mathrm{BMI}=0.20 & \mathrm{BMI}=0.20 \\ \hline \text { After Two Years } & \text { Mean Change in } & \text { Mean Change in } \\ & \mathrm{BMI}=0.71 & \mathrm{BMI}=1.00 \\ & \text { Standard Deviation } & \text { Standard Deviation } \\ & \text { Change in } & \text { Change in } \\ & \mathrm{BMI}=0.28 & \mathrm{BMI}=0.28 \end{array} $$ (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 \(\alpha=0.05\) 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 \(\alpha=0.05\) 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 \(\alpha=0.05\) level of significance. What does this result suggest? (f) To what population do the results of this study apply?

Step by step solution

01

Identify Experimental Design

Determine the type of experimental design based on the description of the study. This is a randomized control trial where participants were randomly assigned to one of two groups to compare their outcomes over time.

02

Identify Variables

Determine the response variable and the explanatory variable. The response variable is the BMI (body mass index), which is being measured. The explanatory variable is the type of intervention, specifically whether participants were in the experimental group or control group.

03

Compare Baseline BMIs

Check if there is a significant difference in BMI between the experimental and control groups at the start using a two-sample t-test. This can be checked using the following formulas:

04

Compute t-Statistic

Using the formulas:

05

Test Statistic Calculation

To test if the mean change in BMI for the experimental group is significantly less than the control group after one year, use the following t-test:

06

One-Year Comparison Conclusion

Based on the p-value obtained from the previous step, determine if the evidence suggests that the change in BMI for the experimental group is less than that of the control group at the 0.05 level of significance.

07

Two-Year Comparison

Conduct a similar t-test to evaluate the change in BMI after two years.

08

Identify Population Applicability

Identify who the results of this study apply to, based on the initial population and sampling method used in the study.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

experimental design

This study uses a **randomized controlled trial** (RCT). Here, researchers randomly assigned 224 overweight adolescents to experimental and control groups. Random assignment helps prevent bias, ensuring that any differences in outcomes between groups are due to the intervention rather than pre-existing differences. The experimental group received an intervention to reduce sugary beverage intake, while the control group received no such intervention.

response variable

In this study, the response variable is **Body Mass Index (BMI)**. BMI is calculated by dividing a person's weight in kilograms by their height in meters squared \( \text{BMI} = \frac{\text{weight (kg)}}{\text{height (m)}^2} \). It is measured at different points to assess the impact of the intervention. Changes in BMI indicate whether there is a weight gain or loss.

explanatory variable

The explanatory variable is the type of intervention received. Specifically, whether participants are in the **experimental group** (who received the intervention to reduce sugary beverage consumption) or in the **control group** (who did not receive any intervention). This variable explains the change in BMI observed.

t-test

The **t-test** helps determine if there are significant differences between the experimental and control groups. For example, to check if there's a difference in BMI at the start, we use a two-sample t-test: \text{t} = \frac{\bar{X1} - \bar{X2}}{s_p\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} \. Here, \( \bar{X1} \) and \( \bar{X2} \) are the sample means of the two groups, \( n_1 \) and \( n_2 \) are the sample sizes, and \( s_p \) is the pooled standard deviation.

BMI comparison

To compare BMI changes, we look at means and standard deviations over time. Initially, the experimental group had a mean BMI of 30.4, while the control group had 30.1. After one year, changes in BMI were 0.06 (experimental) and 0.63 (control). Finally, after two years, BMI changes were 0.71 (experimental) and 1.00 (control). These comparisons help assess the effectiveness of the intervention.

statistical significance

Statistical significance tells us if the results are likely due to the intervention rather than random chance. We use an **alpha level (\( \alpha \)) of 0.05**. If the p-value from the t-test is less than 0.05, the result is considered statistically significant. For example, after one year, if the p-value is low, we conclude that the intervention had a significant effect on reducing BMI compared to the control group.