How to Find a Sample Size Given a Confidence Interval and Width (Known Standard Deviation)

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This article will show you how to determine the appropriate sample size for a given confidence interval and width, given that you know the population standard deviation.

Sample question: Suppose we want to know the average age of an FSCJ student, plus or minus 0.5 years. We’d like to be 99% confident about our result. From a previous study, we know that the standard deviation for the population is 2.9.

Step 1: Find z a/2 by dividing the confidence interval by two, and looking that area up in the z-table:
.99/2 = 0.495.  The closest z-score for 0.495 is 2.58.

Step 2:Multiply step 1 by the standard deviation.
2.58 * 2.9 = 7.482

Step 3:Divide Step 1 by the margin of error. Our margin of error (from the question), is 0.5.
7.482/0.5 = 14.96

Step 4:Square Step 3.
14.96 * 14.96 = 223.8016

Related posts:

  1. How to Find a Sample Size Given a Confidence Interval and Width
  2. How to Find a Confidence Interval for a Mean (Unknown Population Standard Deviation)
  3. How to Find a Confidence Interval for a Mean (Known Standard Deviation)
  4. How to find the sample variance and standard deviation in statistics
  5. How to Find a Confidence Interval For a Sample
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2 Responses to “How to Find a Sample Size Given a Confidence Interval and Width (Known Standard Deviation)”

  1. Angie Widdows said:

    Oct 08, 09 at 8:20 am

    This example is helpful but it seems a little redundant after doing the homework problems. It pretty much states the same thing as the Mathlab. I would not vote this one as better of the examples.

  2. math tutoring said:

    Nov 06, 11 at 8:14 am

    math tutoring…

    [...]Statistics How To» Blog Archive » How to Find a Sample Size Given a Confidence Interval and Width (Known Standard Deviation)[...]…

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