Inference for One Proportion: Determining the Required Sample Size

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I discuss determining the required sample size to achieve a given margin of error in a confidence interval for a population proportion. (For intervals based on the normal approximation.)
  1. jbstatistics
  2. minimum sample size
  3. required sample size
  4. sample size
  5. proportions
  6. one sample proportions
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You're welcome!

p(1-p) is greatest when p = 0.5. This can be illustrated by trying a few values. For example, if p = 0.9, p(1-p) = 0.09, but if p = 0.5, p(1-p) = 0.25.

Using calculus: p(1-p) = p - p^2. The derivative is 1-2p. Setting this equal to 0 and solving for p, p = 1/2. The second derivative is -2, which shows p = 1/2 yields the maximum.

If we don't have any idea of the value of p, we use p = 1/2, as this maximizes p(1-p) and ensures we have a large enough sample size.

jbstatistics
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You're very welcome, and I'm glad to be of help. I still strongly recommend going to class - I'm sure your prof had lots of good stuff to say.

I'm not playing on doing any Markov chain videos in the near future. Once you get into it, you likely won't find it as hard a topic as it might appear at first. And I'm sure some other folks have some videos that might help you understand Markov chains. Cheers.

jbstatistics
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Very nice!
Just don't understand why p=0.5 but I guess that is not in the scope of my course.
Thank you!! Very helpful

bkhosh
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if I have previous incidence and estimate population, which formula should i use for calculating the sample size ?

anaspis