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The population proportion is assumed to be 0.16 . If the desired standard error is 0.0127 or less, what is the minimum sample size
needed?

Ask by Henry Norris. in the United States
Mar 15,2025

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Answer

The minimum sample size needed is 834.

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Beyond the Answer

To determine the minimum sample size needed for a population proportion of 0.16 with a desired standard error of 0.0127 or less, you can use the formula for the standard error of proportion:
Where is the standard error, is the population proportion, and is the sample size. Setting to 0.0127 and to 0.16, you need to solve for :
  1. Plug in the values:
  1. Square both sides:
  1. Rearranging gives you:
  1. Calculate:
Since sample size must be a whole number, round up to 834. Thus, the minimum sample size needed is 834.
So if you’re planning to conduct a survey or an experiment based on this population proportion, make sure to gather a sample of at least 834 individuals to achieve your desired level of precision!

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