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Assume I have 5 millions oranges. Now I want to test a hypothesis.

If there is a black dot on an orange, then the orange is BAD.

Within these 5 millions oranges, I have been told that which are bad.

However, I cannot check all bad oranges to see whether there is black dot on each.

I want to find the sample size that I need to prove my hypothesis is right at 95% sure.

Giordano Fearghas
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2 Answers2

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If I assume a proportion p = .999, an error E of .01 then n for a Z proportion test at the 95% confidence level is:

$$n = 1.96^2 \frac{(.001*.999)}{(.01^2)} = 38$$

Phil H
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  • Would you please also add the name of the test? I want to find more information of the equation. Thanks – Giordano Fearghas Apr 27 '18 at 16:06
  • This is a Z test of significance for a difference in proportion of a single sample. The assumption is the population of bad oranges has a .999 proportion with a black dot, and what sample size is needed to test that assumption at the 95% confidence level. – Phil H Apr 27 '18 at 18:07
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I think you are looking for something like this; http://www.w3computing.com/systemsanalysis/sample-size-decision/

In addition, you can use Chebyshev Inequality.(If you use this, the sample size n will be extremely big!!)

statistic
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