A pollster conducting a telephone poll of a city's residents asked two questions:
1. Do you currently smoke cigarettes?
2. Regardless of your answer to question 1, would you support a ban on smoking in all city parks?
a. Construct a Venn diagram that allows the respondents to the poll to be identified by whether or not they smoke cigarettes and whether or not they support the ban. Choose a reasonable Venn diagram below.
A.
B.
C.
Answer (2)
The problem requires selecting a Venn diagram that correctly represents smokers/non-smokers and those who support/don't support a ban.
Option A is incorrect because it separates smokers and non-smokers instead of showing the overlap with support for the ban.
Option B correctly represents the two categories with overlapping circles for smokers and those who support the ban.
Therefore, the correct answer is B.
Explanation
Understand the problem We are asked to choose a Venn diagram that correctly represents the two categories of respondents: smokers/non-smokers and those who support/don't support the ban. The two categories are 'smokers' and 'support ban'. The Venn diagram should have two overlapping circles, one representing smokers and the other representing those who support the ban.
Analyze the options Option A has two circles, one for smokers and one for nonsmokers. This is incorrect because the two categories are smokers/non-smokers and those who support/don't support the ban. Option B has two circles, one for smokers and one for support ban. This is the correct Venn diagram. Option C has only one circle, which is incorrect.
Choose the correct option The correct Venn diagram is the one with two overlapping circles, one representing smokers and the other representing those who support the ban.
Examples
Venn diagrams are commonly used in market research to understand customer segmentation. For example, a company might survey customers about their preferences for certain product features. A Venn diagram could then be used to visualize the overlap between customers who prefer feature A and those who prefer feature B, helping the company to target its marketing efforts more effectively.
To create a Venn diagram for the smoking poll, we need two overlapping circles: one for smokers and another for supporters of the smoking ban. Option B is the correct choice as it represents both groups and their overlaps accurately. Options A and C are incorrect because they fail to show the required relationships between smoking status and support for the ban.
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