pronouns - Is "My dog can run much faster than I" correct?

I have been revisiting English grammar lessons for a test & I'm reading Pronouns. During a self test I came across this sentence "My dog can run much faster than ___".
I selected "me" & computer said its wrong.

Is "My dog can run much faster than I" correct?

Answer

Yes. Me is an object pronoun, so it doesn't do the action, it receives it. I is a subject pronoun, so it does the action.

In this sentence, both you and the dog are doing the action. Just add can at the end of the sentence and it won't be as confusing.

My dog can run much faster than I can.

Me can't run.

Edit - I must add that regardless of whether or not this is how we speak or if this actually the way we think of it , in the context of an English assessment, this is the right answer and explanation of that answer. Though, in truth most would just say me, even though it is not technically grammatically correct.

(http://www.elearnenglishlanguage.com/blog/english-mistakes/i-vs-me/)