A sentence. If you find any mistakes, please let me know.

Will you go there?
No I won't. I altered changed my mind.

In most cases, "change" and "alter" are interchangeable.  

The ship altered its course.

The ship changed its course.

However, when it comes to "mind".  It cannot be substituted!  "altered my mind" means that your physically have your mind rewired!  Another example

I have changed my address (means that you have moved to a new place)

I have altered my address (means that you are still living in the same place but changed the information for fraudulent or misleading purposes (you don't want to give your real address to a stranger etc)