EXPLORATION 1.2:Tasting Water1 11 Tasting Water EXPLORATION People spend a lot of money on bottled water. But do they really prefer bottled water to ordinary tap water? Researchers at Longwood University (Lunsford and Dowling Fink 2010) investigated this question by presenting people who came to a booth at a local festival with four cups of water. Three cups contained different brands of bottled water, and one cup was filled with tap water.

 

 

 

 

EXPLORATION 1.2: Tasting Water 11 Tasting Water People spend a lot of money on bottled water. But do they really prefer bottled water to ordinary tap water? Researchers at Longwood University (Lunsford and Dowling Fink, 2010) investigated this question by presenting people who came to a booth at a local festival with four cups of water. Three cups contained different brands of bottled water, and one cup was filled with tap water. Each subject (person) was asked which of the four cups of water they most preferred. Researchers kept track of how many people chose tap water in order to see whether tap water was chosen significantly less often than would be expected by random chance. STEP 1: Ask a research question. 1. What is the research question that the researchers hoped to answer? EXPLORATION 1.2 Definition A binary variable is a categorical variable with only two outcomes. Often we convert categorical variables with more than two outcomes (e.g., four brands of water) into binary variables (e.g, tap water or not. In this case we also define one outcome to be a "success" and one to be a "failure" STEP 2: Design a study and collect data. 2. Identify the observational units in this study. 3. Identify the variable. Is the variable quantitative or categorical? 4. Write this as a binary variable. 5. Describe the parameter of interest (in words). (Hint: The parameter is the long-run proportion of...?) 6. One possibility here is that subjects have an equal preference among all four waters and so are essentially selecting one of the four cups at random. In this case what is the long- run proportion (ie, probability) that a subject in this study would select tap water? 7. Another possibility is that the subjects are less likely to prefer tap water than the bottled water brands. In this case what can you say about the long-run proportion that a subject in this study would select tap water? (Hint: You are not to specify a particular value this time; instead indicate a direction from a particular value.)