A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. It is known that the population standard deviation is 8. The instructor has recommended that students devote 3 hours per week for the duration of the 12-week semester, for a total 36 hours. Test to determine whether there is evidence that the average student spent less than the recommended time.

30 40 26 30 36 38 29 40 38 30 35 38

My work:

I have sample, n = 12, mean 34.2, SD = 8, H0 = mu = 36 and H1 = mu < 36 so it is lower tail. And I have z-value = -0.78, p-value is p(z < -0.78) = 0.2177.

Are they correct? How do we figure out the significant level?

Thanks!