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Mathematical problems in calculating two kinds of common error probability in hypothesis testing
Errors of the first kind

H0 is correct, and the statistics belong to the denied domain.

When H0 is true, x = σ Xi ~ p (4), and the probability that the statistic falls into the rejection domain, that is, x = σ Xi = 0, is e (-4).

type ii error

H0 is incorrect, and statistics do not belong to the denied domain.

When H0 is not true, x = σ xi ~ p (2), and the probability that statistics do not fall into the rejection domain is 1-e (-2).

(Note: This question has only formal significance, because H0 and H 1 do not constitute opposing events. )