Simple stats problem: number of tests to be significant?

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SUMMARY

The discussion centers on determining the number of tests required to achieve a 95% confidence level in a binary outcome scenario (Pass/Fail). The Binomial distribution is identified as a suitable statistical model for this situation. Participants suggest utilizing the Central Limit Theorem (CLT) to estimate the mean of multiple independent samples, allowing for the computation of a 95% confidence interval around the sampling mean. This approach provides a robust framework for understanding the significance of test results.

PREREQUISITES
  • Understanding of Binomial distribution
  • Familiarity with Central Limit Theorem (CLT)
  • Basic knowledge of confidence intervals
  • Ability to perform statistical sampling
NEXT STEPS
  • Study the application of Binomial distribution in hypothesis testing
  • Learn how to calculate confidence intervals using sample means
  • Explore statistical software tools for performing simulations (e.g., R or Python)
  • Investigate the implications of sample size on statistical power
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Statisticians, data analysts, quality assurance professionals, and anyone involved in testing and validating binary outcomes in their work.

chaoticfarmin
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Hey guys,

Basically I have a component that I want to test multiple times. The outcome of each test is simply a Pass/Fail. What I want to know is how many tests do I have to do to be (say) 95% sure that I have the right result?

My stats knowledge is a bit hazy but I know that for these type of yes/no situations it may be possible to use the Binomial distribution. Am I on the right tracks?

Cheers if you can help.
 
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This is an idea; I don't know what the real-life constraints you are working with, so here is a general idea: you can use the CLT to estimate the mean: take many random, independent samples (tests, with results of pass/fail, or 1/0) of the same size N: for each sample compute the mean number of sucesses (total successes/total trials). By the CLT, this random variable, the sampling mean, has a normal distribution. Then use a 95% confidence interval about the samplingn mean.
 

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