Help with the following..

4-5 COMPARING TWO MEANS PRE-ACTIVITY 1. a. Are the studies described in Example 1 in the Getting Started section experiments or observational studies? Explain your answer. b. Are the studies described in Example 2 in the Getting Started section experiments or observational studies? Explain your answer. 2. A study was conducted to determine if subjects lose weight while taking a new weight loss product. One hundred volunteers were randomly assigned to receive either the new prod- uct or a placebo product, and weight loss after three months was recorded. a. The population of interest is and the sample is The variable of in- terest is which is (circle one) categorical quantitative and probably has units of b. What kind of study is this? Be specific and explain how you know. 3. To determine whether two brands of oxygen monitors perform similarly, researchers mea- sured oxygen levels using both brands on each of 35 patients, then compared the oxygen readings. a. The population of interest is and the sample is The variable of in- terest is which is (circle one) categorical quantitative and probably has units of b. What kind of study is this? Be specific and explain how you know. 156 Learning Through Practice: Statistical Reasoning4-5 COMPARING TWO MEANS GETTING STARTED LEARNING GOALS Explain and interpret results of a t-test used to compare two population means. Explain the limitations of test conclusions, including practical implications Discern whether a study suggests a cause-and-effect relationship One of the most common statistical questions is whether two groups are the same, on aver- age, or not. Now that we know the reasoning processes of a hypothesis test and a confidence interval, the rest of the module applies these concepts and skills to research questions about differences between two (or more) group means Remember from Module 2 that observational studies and experiments can be done with matched pairs or with independent groups. Matched pair (dependent) data consist of two groups of measurements where each case in group 1 is linked with a specific case in group 2 Links between matched pairs can be anything that links a specific individual in one group with an individual in the other group On the other hand, two independent (unpaired) groups of measurements result from com- pletely randomized experiments (where cases are randomly assigned either a treatment or a placebo) and stratified observational studies (where cases are randomly selected from each of two groups separately) EXAMPLE 1 Among 50 volunteers, a researcher finds two with the same age and health condi tion and flips a coin to choose which one receives the drug vs. the placebo. Each subject receiving the drug has a match, same age and health, that receives the pla- cebo so the data are matched pairs. If instead, researchers randomly assigned each volunteer to either the drug or placebo group, then the data are two independent samples. EXAMPLE 2 A researcher randomly selects twins in which 1 sibling smokes and the other doesn't and measures their lung capacities for comparison. This study is matched pair since the twins are genetically related. The researcher could instead randomly select a group of smokers and separately select a group of nonsmokers; these are two independent groups. Learning Through Practice: Statistical Reasoning 1554-5 Comparing Two Means: Pre-Activity 4. To compare the lengths of two species of North American trout, 20 specimens of each spe- cies were measured and lengths compared a. Is this an observational study or an experiment? observational study experiment b. Are the data matched pair or two independent samples? Explain. 5. To determine the health benefits of a vegetarian diet, researchers used records from 151 sets of twins in which one twin was a vegetarian and one was not. a. Is this an observational study or an experiment? observational study experiment b. Are the data matched pair or two independent samples? Explain. 6. Researchers studied two nutrition programs for malnourished children in a particular re- gion. Supplies were available for 10 randomly selected children to participate in program 1, the rest were assigned to program 2, and percent increase in body weight was measured. a. Is this an observational study or an experiment? observational study experiment b. Are the data matched pair or two independent samples? Explain. NOTES Learning Through Practice: Statistical Reasoning 157