Question

Which of the following statements is correct?

A. We can establish a claim if the sample evidence is consistent with the null hypothesis.
B. We can establish a claim if the sample evidence contradicts the null hypothesis.
C. We can establish a claim if the sample evidence is unrelated to the null hypothesis.
D. We can establish a claim if the sample evidence cannot be determined.

Answer 1

The correct statement about establishing a claim based on sample evidence in hypothesis testing is B. We can establish a claim if the sample evidence contradicts the null hypothesis.

Step-by-step explanation:

The correct statement regarding the establishment of a claim based on sample evidence in the context of hypothesis testing is B. When conducting a hypothesis test, if the sample data is inconsistent with the null hypothesis, we have evidence to reject the null hypothesis, which suggests that the alternative hypothesis may be more likely.

It is important to note that we never state a claim is proven true or false in absolute terms. Hypothesis testing is based on probability laws, and therefore, we can only discuss the likelihood of a hypothesis being supported by evidence. The correct approach to hypothesis testing includes setting up two contradictory hypotheses, collecting sample data, evaluating the data, and concluding whether there is sufficient evidence to reject the null hypothesis based on the analysis performed.