If the $H_0$ (null hypothesis) is rejected in hypothesis testing, which of the following is true?

• A. The $H_0$ (null hypothesis) is proven to be true.
• B. There is sufficient evidence to support the $H_a$ (alternative hypothesis).
• C. The test must be repeated with a larger sample size.
• D. There is not enough evidence to support the $H_a$ (alternative hypothesis).

Answer: (B)

Verified step by step guidance

1. Understand the purpose of hypothesis testing: it is a method to decide whether there is enough evidence in a sample to infer that a certain condition holds for the entire population.
2. Recall the null hypothesis (\(H_0\)) represents the default or status quo assumption, while the alternative hypothesis (\(H_a\)) represents the claim we want to test for evidence.
3. When we reject the null hypothesis, it means the sample data provides sufficient evidence to conclude that the alternative hypothesis is more likely to be true.
4. Rejecting the null hypothesis does NOT mean the null hypothesis is proven true; rather, it means the data contradicts \(H_0\) at the chosen significance level.
5. Therefore, the correct interpretation when the null hypothesis is rejected is: 'There is sufficient evidence to support the alternative hypothesis.'