Handout on Finding the Sample Size Needed for a
Confidence Interval for a Single Population Mean
Table of zvalues for commonly used
confidence levels
 Suppose you want to construct a 95%
confidence interval for the mean age that people have their wisdom teeth
removed. If you know that the standard deviation is
1.8 and you want a margin of error of no more
than plus or minus 0.2 years, at least how many
people must you survey?
Solution
 Past research has shown that the standard deviation for the number of
pencils and pens that college students use in a quarter is
4.2. If you want to construct a
90% confidence interval for the mean number of
pencils and pens that college students use in a quarter and if you want to
have a margin of error of no more than plus or minus
0.3 at least how many students must you survey?
 It is known that that the standard deviation for the number of hours of
sleep that students get each night is 2.1.
If you want to construct a 95% confidence
interval for the mean hours of sleep that students get each night and if you
want to have a margin of error of no more than plus or minus
0.1 at least how many students must you survey?
 You have just conducted a preliminary survey of 22
students asking them how many times a week they eat in fast food
restaurants. The standard deviation for this survey was
2.8. If you want to construct a
95% confidence interval for the mean number of
times per week students eat in fast food restaurant and have a margin of
error no more than plus or minus 0.05, at least
how many additional students must you survey?
Solution
 You have just conducted a preliminary study of 16
gas stations to determine how many cents per gallon their profit is.
The standard deviation for this study was 8.3.
If you want to construct a 95% confidence
interval for the mean cents per gallon that all gas stations profit and have
a margin of error no more than plus or minus 0.5
cents, at least how many more gas stations must you include in your study?
 You have just conducted a preliminary study of 12
people with depression and determined that the standard deviation for the
number of ounces of alcohol that they consume each week is
18 ounces.
If you want to construct a 99% confidence
interval for the mean number of ounces that people with depression consume
per week and have a margin of error no more than plus or minus
2 ounces, at least how many people with
depression must you include in your study?
For questions 7 through 10, answer true or false and give your reasoning.
 Increasing the sample size while holding the level of confidence fixed
will decrease the margin of error for a confidence interval.
Solution
 Decreasing the level of confidence while holding the sample size fixed
will increase the margin of error.
 Tripling the sample size while holding the level of confidence fixed
will decrease the margin of error by a factor of 3.
 If the margin of error is to be decreased by a factor of
2 while holding
the level of confidence fixed, then the sample size must be increased by a
factor of 4.
