What are some resources to test your data science skills? I can't get a job to save my life so I am guessing my lack of skills is an issue. I've been doing a lot of reading on statistics and I am getting antsy - I want to move from theory to application and test my skills to see how I measure up with real practitioners.

Most books I have don't have solutions. They have questions and labs but without some semblance of an answer, I don't know if I am doing it right. I know when it comes to fitting models, there isn't a "right" answer, but there are definitely bad answers. I just want to make sure my answers are good enough.

What are some resources where I can practice my data science, statistical inference, machine learning skills - with answers? I know of https://www.kaggle.com/competitions has tasks but those seem beyond my ability right now - and obviously won't come with right answers.

Are there websites that test your ability to build a predictive model?

Any suggestions?
If you want to move from theory to application then I suggest to do exactly that: get your handy "dirty"!

UCI Machine Learning Repository has some easier datasets to get started. Kaggle is great too but before going for any competition look for an easier dataset from their repository. 

If you prefer something with more guidance the book "Introduction to
Machine Learning with Python" by Mueller and Guido contains many examples starting with the classic Iris dataset. 

Finally, you could consider an online course. The Udacity Nanodegrees include projects which you need to submit so it gives some basic hands-on experience. Though, in your specific case, I would only go this route if you think it might help your CV.