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If I use e=0.05, and from Yamane's formula I obtain, say, a sample size of 300 from given population size. Now, for instance, I obtain some descriptive statistics from the sample size such as the mean value of educated farmers is 20%. Can I interpret 'e' in this context is as I am 95% confident that the mean of the educated farmers in the population is 20%. or interchangeably, on average the number of educated farmers in the population is 20% (+ - 5%): i.e, (20%+5%) & (20% -5%). so technically between 15% and 25%.

The formula I used is:n = N/(1+N (e)^2)

n =  sample size
N = Total population size
e = precision level 5% (0.05):

Or does that mean, ' the sample size of 300 (±5%) truly/accurately represents the given population size?

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    $\begingroup$ Please edit your question to give & explain the formula you're referring to. (It's entirely possible that someone writes it with f instead of e, or uses e for another variable). $\endgroup$
    – Scortchi - Reinstate Monica ♦
    Commented Sep 12, 2021 at 13:51
  • $\begingroup$ Hello Monica, I have added a photo of the formula, I am not sure If it is visible to you or not? $\endgroup$
    – Jamal Shah
    Commented Sep 12, 2021 at 14:13
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    $\begingroup$ That hasn't worked. In any case, I'd suggest typing the formula, using LaTeX if you know it - for the sake of visually impaired people using screen readers, among other reasons. $\endgroup$
    – Scortchi - Reinstate Monica ♦
    Commented Sep 12, 2021 at 14:19

1 Answer 1

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e=0.05 transforms a sample's value to ±5% of the population's value.

This is how e is interpreted in Yamane/Cochran formulae. See the excerpt and reference below for an explanation on the error margin's use and interpretation.

NB: All other statistical/data collection procedures should be correct for that interpretation (assumption) to be true.

The level of precision, sometimes called sampling error, is the range in which the true value of the population is estimated to be. This range is often expressed in percentage points, (e.g., ±5 percent).

Thus, if a researcher finds that 60% of farmers in the sample have adopted a recommended practice with a precision rate of ±5%, then he or she can conclude that between 55% and 65% of farmers in the population have adopted the practice.

Source: Israel, G. D. (1992). Determining sample size. Fact Sheet PEOD-6. University of Florida. (pdf)

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