When is that being used as a connection for an embedded sentence
I think he is happy
I think that he is happy
What is the difference? When is that used and not used?
and scroll down to rubric 3. "Noun Clauses that Start with That."
You can often drop the that from these sentences. If it makes sense, drop it. It's more of an oral (spoken) crutch - it's not required in written text. Not incorrect, just unnecessary.