Variation in Sample Proportions (Example 7) Suppose it is known that 20 % of students at a certain college participate in a textbook recycling program each semester. a. If a random sample of 50 students is selected, do we expect that exactly 20 % of the sample participates in the textbook recycling program? Why or why not? b. Suppose we take a sample of 500 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to 20 % : the proportion from a sample size of 50 or the proportion from a sample size of 500 ? Explain your reasoning.
Variation in Sample Proportions (Example 7) Suppose it is known that 20 % of students at a certain college participate in a textbook recycling program each semester. a. If a random sample of 50 students is selected, do we expect that exactly 20 % of the sample participates in the textbook recycling program? Why or why not? b. Suppose we take a sample of 500 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to 20 % : the proportion from a sample size of 50 or the proportion from a sample size of 500 ? Explain your reasoning.
Solution Summary: The author determines whether a sample's proportion of participants in the book recycling program is equal to " 20% or not.
Variation in Sample Proportions (Example 7) Suppose it is known that
20
%
of students at a certain college participate in a textbook recycling program each semester.
a. If a random sample of 50 students is selected, do we expect that exactly
20
%
of the sample participates in the textbook recycling program? Why or why not?
b. Suppose we take a sample of 500 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to
20
%
:
the proportion from a sample size of 50 or the proportion from a sample size of
500
?
Explain your reasoning.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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Part (b)
Draw a scatter plot of the ordered pairs.
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Life
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Life
Expectancy
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Life
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Part (c)
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Year of
2010 Birth
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Harvard University
California Institute of Technology
Massachusetts Institute of Technology
Stanford University
Princeton University
University of Cambridge
University of Oxford
University of California, Berkeley
Imperial College London
Yale University
University of California, Los Angeles
University of Chicago
Johns Hopkins University
Cornell University
ETH Zurich
University of Michigan
University of Toronto
Columbia University
University of Pennsylvania
Carnegie Mellon University
University of Hong Kong
University College London
University of Washington
Duke University
Northwestern University
University of Tokyo
Georgia Institute of Technology
Pohang University of Science and Technology
University of California, Santa Barbara
University of British Columbia
University of North Carolina at Chapel Hill
University of California, San Diego
University of Illinois at Urbana-Champaign
National University of Singapore
McGill…
Name
Harvard University
California Institute of Technology
Massachusetts Institute of Technology
Stanford University
Princeton University
University of Cambridge
University of Oxford
University of California, Berkeley
Imperial College London
Yale University
University of California, Los Angeles
University of Chicago
Johns Hopkins University
Cornell University
ETH Zurich
University of Michigan
University of Toronto
Columbia University
University of Pennsylvania
Carnegie Mellon University
University of Hong Kong
University College London
University of Washington
Duke University
Northwestern University
University of Tokyo
Georgia Institute of Technology
Pohang University of Science and Technology
University of California, Santa Barbara
University of British Columbia
University of North Carolina at Chapel Hill
University of California, San Diego
University of Illinois at Urbana-Champaign
National University of Singapore…
Chapter 7 Solutions
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