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Handout on Finding the Sample Size Needed for a
Confidence Interval for a Single Population Proportion
Table of z-values for commonly used
confidence levels
- Suppose you want to construct a 95%
confidence interval for the proportion of college students who floss daily.
You want a margin of error of no more than plus or minus
3%. According to the ADA
12% of all Americans floss daily. If you think that college
students' flossing habits are similar to the general population of
Americans, how many college students should you survey?
Solution
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15% of all homes in California will collapse in
a major earthquake. I you want to construct a 99%
confidence interval for the proportion of all homes in El Dorado county that
will collapse in a major earthquake such that the margin of error is no more
than plus or minus 2%, how many homes must you
include in your study?
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Last week, you surveyed 100 college students and
found that 78% of them went to at least one
party in the last 7 days. If you want a
margin of error of no more than plus or minus 4%,
how many more students do you need to survey in order to construct a
95% confidence interval for the proportion of
all college students who went to at least one party in the last
7 days?
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Suppose you want to construct a 90% confidence
interval for the proportion of college students that want to work in the
health care profession after graduation. If you want a margin of error
of no more than 5%, how many college students
must you survey?
Solution
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Suppose you want to construct an 80% confidence
interval for the proportion of business that provide incentives to carpool
to work. If you want a margin of error of no more than
3.5%, how many businesses must you survey?
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If you want to find a 95% confidence
interval for the proportion of Californians who would consider taking a high
speed train for traveling if there were a station in their neighborhood and
you want a margin of error of no more than plus or minus
3%, how many Californians must you survey?
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