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Why is the test size equal to the false discovery rate only when the null hypothesis...

Why is the test size equal to the false discovery rate only when the null hypothesis is correct? I may be misunderstanding what test size means. Also, is the false discover rate just the number of type 1 errors divided by the total number of rejected null hypotheses? If a set of rejected null hypotheses was rejected under a test of a 5% size, does this mean that out of all these hypotheses only 5% of them are actually true? Thank you for the help!

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