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.
Elementary Statistics: Picturing the World (7th Edition)
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