Last year, there were 30,000 students at a university; their GPA had a mean of 2.9 and an SD of 0.6. This year, in a simple random sample of 100 students taken from this university, the GPAs have a mean of 2.95 and an SD of 0.55. Has the mean GPA at the university gone up since last year, or is this just chance variation?

one-sample z = (2.95 - 2.9)/0.06 = 0.833; P large; conclude chance variation one-sample z = (2.95 - 2.9)/0.055 = 0.909; P large; conclude chance variation two-sample z = (0.05 - 0)/sqrt(0.055^2 + 0.0035^2) = 0.907; P large;

Question

Last year, there were 30,000 students at a university; their GPA had a mean of 2.9 and an SD of 0.6. This year, in a simple random sample of 100 students taken from this university, the GPAs have a mean of 2.95 and an SD of 0.55. Has the mean GPA at the university gone up since last year, or is this just chance variation? 

one-sample z = (2.95 - 2.9)/0.06 = 0.833; P large; conclude chance variation one-sample z = (2.95 - 2.9)/0.055 = 0.909; P large; conclude chance variation two-sample z = (0.05 - 0)/sqrt(0.055^2 + 0.0035^2) = 0.907; P large;