The problem that I'm working on is this:
We've got a random sample of iid $X_1, ..., X_n$ with distribution $N(\mu,1)$ and let $S_n=X_1+...+X_n$. Find the significance level (p-value) for $S_n$ testing $H_0: \mu = 3$ and $H_1:\mu=6$, for $n=4$ and $S_4=15$.
So far I've used the Neyman-Pearson lemma and got this result: $\sum\limits_{i=1}^4 x_i\geq\frac{logK}{3}+18\hspace{2mm}$ if my calculations are correct.
And from there I don't know how to continue, I guess I should use $S_4$ somehow. I've been thinking about dividing everything by 4 and then I'll get some inequality for $\overline{x}$.