Das maximale signifikanzniveau des Tests: “LehneH _o ab, wennk untern gegebenen tests zur ablehnung führen”

Summary

On one sample space there aren tests with critical regionsK ₁ and levels of significance α _i ,i=1, ...,n (resp.n eventsK _i in a probability space with probabilities not greater than α _i ,i=1, ...,n). In this paper we calculate the smallest upper bound of the level of significance of the test “reject the hypothesis, if at leastk among the,n tests do so” (resp. of the probability of the event “at leastk among then events are realized”). By the way, we will show, that this smallest upper bound does not change, if we replace “at leastk” by “exactlyk.”