Help - How do you calculate Z scores given mean and standard deviation?

#1
I need to calculate z(obs) when given mean and standard deviation from a population and one sample, as in μ0 =32, σ0 =10, m=27, and n=25, assuming H1: μ1 − μ0 < 0. What would I do differently assuming H1: μ1 − μ0 ≠ 0? Thank you for an help provided.
 
#3
To calculate p, I could use a z table, then double my answer if assuming H1: μ1 − μ0 ≠ 0? For this problem, I found z = 2.5 and p = .0062 if H1: μ1 − μ0 < 0 and p = .0124 if H1: μ1 − μ0 ≠ 0. Is this correct?