I just realize the text did not appear properly: here is the correct:

Let X be a Normal random variable N (μ, σ2= 169) with an unknown parameter μ. For testing the hypothesis H0: μ = 28 versus H1: μ = 31 a random sample of size n = 225 is observed.

a) Consider the following rejection region: RX_mean>= 29.1107) evaluate the probability alpha of the type I error(reject H_0 when H_0 true) and β (the probability of the type II error= accept H_0 when H_0 false) corresponding to the given test.

b) Calculate the p-value corresponding to the following sample:

(32, 29, 28, 34, 27)

Point a) is okay.

For the point b) my teacher wrote P[Z>=(30-28)/(13/15)]

I do not understand why she used 15 when the new sample is 5 ?

Thank you.

Please help. Exam tomorrow.