"Дякую, я не голодна."

Translation: Thank you, I am not hungry.

[Conrad979215]

Why is голодна used?

[JameLanguaged]

Should 'no thank you, I'm not hungry' be accepted?

[max.goncharuk]

I know that double "no" in same sentence is not preferred in English. So, may be "No, thank you. I'm not hungry" will correct and pretty same but there will be two sentences.

[Sr.Cisne]

I don't believe your example would be two sentences Max, but a simple sentence with an introductory dependant clause.