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I've recently start learning methods for determining whether or not time series are stationary. The first method I'm trying to learn is the 'Dickey-Fuller Test'. This test uses a time series modeled by an AR(1) process. The key is to find whether or not this process contains a unit root. If it contains a unit root, the series is said to be non-stationary.

While I'm understanding most of the derived equations, I'm inexperienced in hypothesis testing. Thus I'm struggling with the part when we actually implement the Dickey-Fuller test. There do not seem to be many resources that outline the iterative process for conducting the test.

I've outlined my question in full here:

http://imgur.com/HMWtn59

I appreciate any help!