Btukfyl

That is what I've got so far, but I have no idea how to insert the arrow. I would really appreciate any kind of help! Thanks again to @marmot

documentclass[tikz,border=3.14mm]{standalone} 



begin{document}    

begin{tikzpicture} 

draw[-stealth] (-4,0) -- (-4,4.5);

draw[blue] plot[variable=x,smooth,domain=-4:4] (x,{2-2*tanh(1.5*(x+1))}) node at (-1.3,3) [left]{G"utefunktion}; 

draw[-stealth] (-4.5,0) -- (4.5,0) node[below right]{$mu$};          

 draw[black,thick] (0.25,-0.5) -- (0.25,5) node at (0.25, -0.5)[below]{140};

 draw[-latex] (0.5,4.5) -- (4,4.5) node[midway,above]{H0 Bereich};

 draw[-latex] (-0.05,4.5) -- (-4,4.5) node[midway,above]{H1 Bereich};

draw [red] (-4.2,0.5) -- (3,0.5) node at (-4.3,0.5) [left]{$alpha$ = 0,05};

draw [black] (-4.2,4) -- (4.5,4) node at (-4.2,4) [left]{1};    

end{tikzpicture} 

end{document}

Actually with shade, drawing the arrow is not really complicated. However, the text is not really readable IMHO.

In this answer, I don't use tang function, but a simple curve using in and out. This helps me calculate the coordinates for drawing the arrow.

Next time you ask a question, please make sure that you put some efforts into solving it in advance, otherwise it is very likely that your question is closed (like this one).

documentclass[tikz]{standalone} 

usetikzlibrary{intersections,decorations.markings}

usepackage{amsmath}

begin{document}    

begin{tikzpicture}[scale=5,>=stealth]

draw[<->] (0,1.1) -- (0,0) coordinate (o) -- (1.75,0) coordinate (x) node[below] {$mu$};

path (0,1) coordinate (y);

draw (-.02,1) node[left] {$1$}--(.02,1);

draw (-.02,0) node[left] {$0$}--(0,0);

draw[name path=alpha,red] (-.1,.05) node[left] {$alpha=0.05$}--(1.75,.05);

draw[name path=curve,blue,postaction={

    decorate,

    decoration={

        markings,

        mark=at position 0.5 with coordinate (midarrow);,

        mark=at position 0.55 with coordinate (nodename);

    }

}] (0,1) to[out=0,in=180] (1.5,0);

path[name intersections={of=curve and alpha,by=inter}];

draw (inter) -- (inter |- o) -- ++ (0,-.1) node[below] {$140$};

draw (inter) -- (inter |- y) -- ++ (0,.2);

draw (y) -- ++ (1.75,0);

draw[->] ([shift={(-.02,.05)}]inter |- y) node[above left] {$H_1$-Bereich} -- ++ (-.5,0);

draw[->] ([shift={(.02,.05)}]inter |- y) node[above right] {$H_0$-Bereich} -- ++ (.5,0);

path[blue] (nodename) node[below left] {G"utefunktion};

path (o)--(y) node[midway,sloped,above,font=footnotesize] {$g(mu)=P(text{Ablehnung von }H_0)$};

shade[top color=yellow!60!black,bottom color=yellow] (midarrow) -- ++(.1,.1) --++(-.05,0) --++(0,.15) --++(-.1,0) --++(0,-.15) --++(-.05,0) --cycle;

shade[top color=yellow,bottom color=yellow!60!black] ([shift={(.05,.25)}]midarrow) --++(0,.15) --++(.05,0) --++(-.1,.1) --++(-.1,-.1) --++(.05,0) --++(0,-.15) -- cycle;

path[yellow!20!black] (midarrow) --++(0,.25) node {Some text};

node at (0,1.25) {$H_0:;mugemu_0$};

end{tikzpicture} 

end{document}