EXPLORATION 1.2:Tasting Water1 11 Tasting Water EXPLORATION People spend a lot o

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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. Each subject (person) was asked which of the four A binary variable s a cups of water they most preferred. Researchers kept track of how many people chose tap categorical water in order to see whether tap water was chosen significantly less often than would only two outcomes. Often be expected by random chance 1.2 we convert catogorical variables with more than two outcomes (eg., four brands of water) into binary variables (e.g. tap water or non-inthis e we also define one outcome to be a success" and one to be a STEP 1: Ask a research question. 1. What is the research question that the researchers hoped to answer STEP 2: Design a study and collect data 2. Identify the observational units in this study Identify the variable. Is the variable quantitative or categoricalh 3. 4. Write this as a binary variable. 5. Describe the parameter of interest (in words). (Hint: The parameter is the long-run proportion of ...?) 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? 6. 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.) 7. Another possibility is that the subjects are less likely to prefer tap water than the botled

Explanation / Answer

1)

Research Question:

Do people prefer Tap water or Bottled Walter?

2)

Tap Water Choice of each subject is recorded.

Tap Water: True if the subject chose Tap Water else False

3)

Variable: Tap Water

The Variable is categorical.

4)

Tap Water: 1 if the subject chose Tap Water else 0

5)

The Parameter of interest is the long run proportion of subject who prefer tap water to bottled water.

6)

This will be simply the probability of selecting the tap water cup which is ¼ or 0.25

7)

In the long run, the proportion of people who prefer bottled water is more than proportion of people who prefer tap water.

8)

Null Hypothesis (H0): The proportion of people who prefer tap water is same as those who prefer bottled water.

Alternate Hypothesis (Ha): The proportion of people who prefer tap water is not as same as those who prefer bottled water.

9)

Given, 3 out of 27 selected tap water.

Proportion of tap water (p1) = 3/27 = 0.11

Proportion of bottled water (p2) = 1-0.11 = 0.89

N = 27

Standard Dev (s) = sqrt(p*(1-p)/n) = 0.06

Therefore, Test Statistic:

Z = (p1-p2-(µ1 - µ2))/s = -12.86

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