Use a large sample when individual times need not be normal

A large number of students in a college have completed a geography project. The time, $x$ hours, taken by a student to complete the project is noted for a random sample of 150 students. The results are summarised by $\sum x=4626$, $\sum x^2=147691$.

Find unbiased estimates for the population mean and variance.

Test, at the 5% significance level, whether the population mean time for a student to complete the project exceeds 30 hours.

State, giving a reason, whether any assumption about the population is needed for the test to be valid.