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Finding Sample Size with Predetermined Margin of Error and Level of Confidence for a Mean

Finding Sample Size with Predetermined Margin of Error and Level of Confidence for a Mean

Author: Al Greene

• Demonstrate how to use the margin of error formula (t*(n-1)• S ) to calculate sample size when given a predetermined margin of error and level of confidence for a one-sample t-interval
• Review standard error for means

This packet is similar to the packet on estimating a sample size for proportions. We show you how to calculate a desired sample size given a margin of error and confidence level.

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What's in this packet

This packet covers sample size estimation when you are given a margin of error and confidence level for a means problem. There is a powerpoint of definitions and examples, as well as examples for you to do on your own. There are no new terms in this packet.

Source: Greene

Sample Size Estimation

This powerpoint breaks down the sample size estimation formula, and gives a short example of how to use it.

Source: Greene

Sample Size Point Estimate Statistics

This video shows two examples on estimating a desired sample size based on predetermined margins of error.


Suppose we have a population with a standard deviation of 17. We would like to create a 99% confidence interval with the margin of error being at most 5. What should our sample size be?









For our formula, we have a standard deviation of 17, a multiplier of 2.576(from the powerpoint), and a margin of error of 5. Therefore, we have


n = ((2.576*17)/5)^2 = 8.7584^2 = 76.7096 which we will round up to 77.

Therefore, a sample of size 77 will ensure our margin of error for our confidence interval is no greater than 5.

Source: Greene