A person claims that he can differentiate if a medicine is working or a placebo. Therefore we test the null hypothesis $p=0.5$ and $\alpha=0.5$ with $n=50$ with a right handed hypothesis test.
Edit: The rest of the question says: how likely is a type ii error if the person can actually distinguish between working medicine and placebo by an accuracy of 70%.
The question is about : Does the person just guess or does the person really have the ability to distinguish between a placebo and working medicine.
How do I define the null hypothesis numerically ?
updated thoughts:
Since we have a right handed test, we try to see what upper area will lead us to deny a hypothesis.
H0 : The person can not distinguish between placebo and medicine
H1 : The person can distinguish between placebo and medicine