Three factories produce the same screws with different percentages of defective products, e.g., a, b, and c. I came into one of them but didn't know which one I had come into. I could only defect the products the one produced. So how many samples do I need to determine which factory I came into? Maybe the statistical power $1−\beta$ and significance level $\alpha$ are required.
I have tried to use an A/B test tool at https://www.evanmiller.org/ab-testing/sample-size.html to calculate the sample size. But it is used to compare two populations. And I don't know how to transform the percentages of defective products to the minimum detectable effect.
I think we can carry out three groups of hypothesis :h_0_a:go into a ,h_1_a:do not go into a.With alpha ,we can know the smallest number that you need to pick in a,b,c respectively.And then we can let the biggest number among them.