TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2020W/HW08.1

t-test

In the context of a one-sample t-test let ${\textstyle {\bar {x}}=2.05,\ s^{2}=4,\ n=16}$ and $H_{0}:\mu =1$. The values of the distribution function F of the t(n)-distribution are

How do you decide

(a) at a right-sided test at level 5%?

(b) at a right-sided test at level 1%?

(c) at a left left-sided test at level 5%?

(d) at a two-sided test at level 5%?

Briefly explain your choice. (Only use the upper information)

Lösungsvorschlag von Friday

--Friday Sa 30 Jan 2021 17:19:14 CET

$$t={\frac {{\overline {x}}-\mu _{0}}{s/{\sqrt {n}}}}\approx {\frac {2.05-1}{2/4}}=2.1$$

$$p=0.027$$

Part a)

$$\alpha =0.05$$

Reject hypothesis because ${\textstyle p\leq \alpha }$.

Part b)

$$\alpha =0.01$$

Do not reject hypothesis because ${\textstyle p>\alpha }$.

Part c)

$${\begin{aligned}\alpha &=0.05\\1-p&=0.973\end{aligned}}$$

Do not reject hypothesis because ${\textstyle (1-p)>\alpha }$.

Part d)

$${\frac {\alpha }{2}}=0.025$$

Do not reject hypothesis because ${\textstyle p>{\frac {\alpha }{2}}}$.