Final answer:
The null hypothesis is assumed to be true and rejected only if outcomes are extremely unlikely, indicating the answer is D) Assumed; true; extremely unlikely. The alternative hypothesis is supported when the null is rejected, but absolute certainty is not obtained—only probabilistic conclusions.
Step-by-step explanation:
The null hypothesis is assumed to be true and is only rejected when the observed outcome is shown to be extremely unlikely. This means that the correct answer to the fill-in-the-blank question is D) Assumed; true; extremely unlikely. The null hypothesis is an assumption about a population parameter that serves as the starting point for statistical testing. When we perform a hypothesis test, we use sample data to determine the likelihood of observing such data if the null hypothesis is indeed true.
Rejecting the null hypothesis implies that there is sufficient evidence to support the alternative hypothesis, which is a statement contrary to the null hypothesis. Therefore, the answer choices referring to proving something as unequivocally true or false are incorrect, as scientific hypothesis testing is a matter of assessing probabilities, not certainties.
Rare events that are highly improbable under the assumption of the null hypothesis can lead to its rejection. However, it is important to keep in mind the possibility of errors, specifically a Type 1 error, where you might reject a true null hypothesis, or a Type 2 error, where you might fail to reject a false null hypothesis.