TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Levajkovic)/Übungen 2023W/HW07.2

Interpretation of results

In the context of a statistical test at significance level $\alpha$, the test statistic lies in the rejection region. Comment on the following statements.

(a) The null hypothesis is rejected at the $\alpha$-level

(b) The null hypothesis is rejected at the $\alpha$/2-level.

(c) The null hypothesis is rejected at the 2$\alpha$-level.

(d) The $p$-value was at least $\alpha$.

(e) The null hypothesis was significant.

(f) The null hypothesis is not true.

(g) The null hypothesis is probably not true.

Dieses Beispiel ist als solved markiert. Ist dies falsch oder ungenau? Aktualisiere den Lösungsstatus (Details: Vorlage:Beispiel)

Lösungsversuch von Simplex

(a)

False, because according to the slides:

Reject $H_{0}$ if and only if $z\in R$

In the assignment it is written, that "the test statistic ($z$) lies in the rejection region".

(b)

Unknown

(c)

True, because the rejection region gets bigger and the null hypothesis already got rejected at $\alpha$. From the slides:

It is self-delusive to increase $\alpha$ in order to reject!

(d)

False, because already known from (a): was rejected. According to the slides:

$p\leqslant \alpha$ $\leftrightarrow$ incompatible enough $\leftrightarrow$ reject null hypothesis

Because $\alpha$ got rejected, $p\leq \alpha$ and therefore p is not at least $\alpha$.

(e)

False, according to the slides, when rejected we say, that the discrepancy was significant. There is no appearance that the null hypothesis was significant.

(f)

False, no statement can be made about the falseness of the null hypothesis.

(g)

False, no statement can be made about the falseness of the null hypothesis.

--Simplex 19:46, 3. Feb. 2023 (CET)