This is very basic frequentist statistics, for which the packages have been mature for years.
You may want to pay attention to calling conventions though, some functions might work differently — eg use the standard deviation instead of the variance, and similar. Better make sure you understand the theory and check the docs. ANOVA may be a tricky point, since they are so many subtly different ways to do it.
FWIW, as much as I like Julia, I would just stick to the language used by the course and use the time I save to do a fun project in Julia. It is unlikely that there will be a lot of programming involved at this level, the computer should just serve as a sophisticated calculator and plotting tool.