Are Undergraduate Statistics Concepts Used in Practice?
t-test and ANOVA are used pretty often, more in statistical data analysis which is a "must know" for a data scientist but not necessarily their everyday work. More you go toward medical/bio statistics or social sciences, you see them more used. 

In everyday life of a data scientist, the problem of feature selection, for example, is one of situations where ANOVA helps. For instance imagine numerical features and discrete classes in a classification problem. A way to select good features is to compare the distributions of features values for each class and see if those distributions differ significantly.

I also have used Wilcoxon test once in a low-sample size project where I was trying to recognize patterns in Complex Networks, created from time-series of two control groups. The story was to see which features of those networks (centrality measures, clustering coefficient, average path length, etc.) makes the significant difference (so can be used for recognition i.e. classification problem). 

This difference was the difference between distribution of feature values among those two groups where those distributions were not necessarily Gaussian. Wilcoxon helped a lot there, as some bold difference between two groups for certain features were actually statistically not significant and without such test the analysis could go the wrong way.

Hope it helped!