What is the minimum number of tests to achieve statistical significance? I'm dealing with a situati

rose2904ks

rose2904ks

Answered question

2022-06-30

What is the minimum number of tests to achieve statistical significance?
I'm dealing with a situation where in a large manufacturing facility we have approximately 2000 plumbing fittings of the same make and model. 3 of those fitting have failed within the last year. Each causing major property damage. We suspect that the plumbing components suffered degradation and we want to test a sample of the remaining plumbing components to see how wide spread the issue is (if at all).
What is the best way to decide how big of a sample we should choose so that we do not under test or over test the installed components.
Any idea where to begin?

Answer & Explanation

kejohananws

kejohananws

Beginner2022-07-01Added 19 answers

Take p ¯ = 3 2000 = 0.0015 , q ¯ = 1 p ¯ = 1 0.015 = 0.9985
If you want the confidence level to be 95% which is typical for hypothesis testing with the margin of error within say 5% of the population proportion of failed fittings of all the fittings, then z c = 1.96
Thus the sample size n you need is
n = z c 2 p ¯ q ¯ E 2 = 1.96 2 0.0015 0.9985 0.05 2 = 2.3 n = 3
Thus you should take a minimum of 3 fittings for a test run. The number might be ridiculously small, but hey it works !

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