help? hypothesis test selection and execution

#1
Hi. I am trying to figure this out and I'm not sure if I am doing it right.
a) did I select the correct type of hypothesis testing???
b) am I using the numbers in the right place (I have SD for 3.5 for pop and 2.86 for sample. which one is right for my hypothesis and equation?)
c) what else am I doing wrong?

The general population gets 8 hours of sleep with a standard deviation of 3.5

My sample group (n=20) gets 8.84 hours with a standard dev of 2.86

I think the general population actually gets more than 8 hours so I need to develop and test a hypothesis. Ho < 8 and Ha >= 8
This will be a one tailed test with alpha of 0.05 so my z score is +1.65

(8.84-8)/3.5/(sqrt 20) = 0.84/0.78 = 1.08

1.08 is not within the critical region and I can not reject the null hypothesis.

THANKS in advance for any advice you can offer!!!