**Explanation:**

The correct answer to the sentence "I don't think Natalie ---- (study), she was out all day" is "was studying."

**Subject-Verb Agreement:**

In this sentence, we are talking about Natalie and her activities. The subject "Natalie" is a singular noun, so we need to use the singular form of the verb.

**Progressive (Continuous) Tense:**

The verb "study" can be used in the progressive (continuous) tense by adding the auxiliary verb "was" before it. The progressive tense indicates an ongoing action in the past. In this case, we are talking about Natalie studying in the past while she was out all day.

**Negative Statement:**

The sentence starts with "I don't think," indicating a negative statement. When making a negative statement in the past, we use the negative form of the auxiliary verb "do" (in this case, "do" becomes "did") before the main verb. However, in the progressive tense, we use the negative form of the auxiliary verb "be" (in this case, "be" becomes "was") before the main verb.

**Putting it all together:**

Considering the subject-verb agreement, the tense, and the negative statement, we can conclude that the correct answer is "I don't think Natalie was studying, she was out all day." This sentence indicates that the speaker believes Natalie was not studying because she was out all day.