Overview
I'm working on a mathematics question and need an explanation and answer to help me learn.
The Application:
A survey was conducted by Yahoo News and Marist College.* A total of 1,122 adults were polled
between March 1st through March 7th, 2017. The survey consisted of adults 18 years of age and older
residing in the contiguous United States were contacted on landline or mobile numbers and interviewed
in English or Spanish by telephone using live interviewers. Mobile telephone numbers were randomly
selected based upon a list of telephone exchanges from throughout the nation from Survey Sampling
International. The exchanges were selected to ensure that each region was represented in proportion to
its population. Mobile phones are treated as individual devices. To increase the representativeness of
traditionally under-covered survey populations, this mobile sample was supplemented by respondents
reached through random dialing of landline phone numbers from ASDE Survey Sampler.
The following are two of the survey questions asked,
1. Have you tried marijuana at least once in your lifetime?
2. Do you support the ban of marijuana in the United States?
The results of the 1122 participants are that 573 answered yes to question 1, indicating that they had
tried marijuana in their lifetime, 512 answered yes to question 2, indicating that they supported
legislation for the continued ban of marijuana in the United States, and 63 answered yes to both
questions, indicating that they had tried marijuana in their lifetime and support the continued ban of
marijuana in the United States. The remaining 100 participants answered no to both questions,
indicating that they had not tried marijuana and did not support the ban.
Instructions:
Create a Venn diagram to represent the survey results in terms of the two survey questions and
possible outcomes (Yes/No, Yes/Yes, No/Yes, and No/No). Be sure to label each region of the Venn
diagram, and to discuss what each region of the Venn diagram represents as it relates to
marijuana usage and the continued ban of marijuana in the United States. Be sure to refer to the Venn
diagram to make conclusions about each of the regions and the relationship of the regions to each other.
The narrative needs to show the relationship between your Venn diagram and your conclusions. The
response should be approximately 250 words and use grammatically correct sentence structure.
Questions to Address While Writing Your Report:
1. Discuss whether this poll is a valid sample as it relates to the current population of the United
States. Is the survey a random sample that represents the general population? Should any other
factors have been considered when conducting this poll?
2. Discuss which region represents those who have tried marijuana in their lifetime and support the
ban? Tried marijuana in their lifetime and do not support the ban? Not tried marijuana in their
lifetime and support the ban? Not tried marijuana and do not support the ban?
3. Discuss the regions that represent those who have tried marijuana in their lifetime and not tried.
Support the ban versus not supporting the ban.
4. What is the difference between “trying marijuana and supporting the ban,” and “trying marijuana or
supporting the ban”?
5. Your response should include calculations and use words like union, intersection, complement.
State the reasoning used in your organization and interpretation of the data.