rose2904ks

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?

kejohananws

Take $\overline{p}=\frac{3}{2000}=0.0015,\overline{q}=1-\overline{p}=1-0.015=0.9985$
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
$n=\frac{{z}_{c}^{2}\cdot \overline{p}\cdot \overline{q}}{{E}^{2}}=\frac{{1.96}^{2}\cdot 0.0015\cdot 0.9985}{{0.05}^{2}}=2.3\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}n=3$
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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