TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/9.6

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Which statement is correct?

In the situation of an ANOVA with k groups of k observation each, assume that the null hypothesis H_0 : \mu_1 = \cdots = \mu_k was rejected on the 1%-level. Comment on the following statements.

(a) The rejection boundary is derived from the F(k − 1, (k − 1)k)-distribution
(b) The test statistic f exceeded the 1%-Quantile of the associated F-distribution
(c) The test statistic f exceeded the 99%-Quantile of the associated F-distribution
(d) The null hypothesis is also rejected on the 5% level
(e) With probability less than 5% we obtain a value of the associated F-statistic that is greater than the observed f, if the null hypothesis is true.
(f) If the null hypothesis was not true, we would have neither made the α- nor the β-error
(g) We can not conclude that at least two expectations µi and µj are unequal) Distribution of the-value in simulations

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