In hypothesis testing, if the $H$₀ is rejected, which of the following is true?

• A. There is sufficient evidence to support the alternative hypothesis.
• B. The test statistic falls within the acceptance region.
• C. The probability of a $\mathrm{Type} 1$ error is zero.
• D. The $H$₀ is proven to be false.

Answer: (A)

Verified step by step guidance

1. Understand the null hypothesis (H0) and alternative hypothesis (H1): H0 represents the default assumption, while H1 represents the claim we want to test for evidence.
2. Recall that rejecting the null hypothesis means the sample data provides enough evidence to support the alternative hypothesis, but it does not prove H0 is false with absolute certainty.
3. Recognize that the test statistic falling within the acceptance region means we do not reject H0, so this is not true when H0 is rejected.
4. Know that the probability of a Type I error (rejecting H0 when it is true) is equal to the significance level \( \alpha \), not zero, so this statement is false.
5. Conclude that rejecting H0 means there is sufficient evidence to support H1, but it does not prove H0 is false; hypothesis testing is about evidence, not proof.