True or False: Sample evidence can prove a null hypothesis is true.

Verified step by step guidance

1. Understand the role of the null hypothesis (denoted as \(H_0\)) in hypothesis testing: it is a statement that there is no effect or no difference, and it serves as the default assumption.
2. Recognize that in hypothesis testing, we collect sample evidence to assess whether there is enough evidence to reject the null hypothesis, not to prove it true.
3. Recall that failing to reject the null hypothesis does not mean we have proven it true; it simply means there is insufficient evidence against it based on the sample data.
4. Understand that statistical tests are designed to control the probability of incorrectly rejecting a true null hypothesis (Type I error), but they do not confirm the truth of \(H_0\).
5. Therefore, the correct interpretation is that sample evidence can lead us to reject or fail to reject the null hypothesis, but it cannot prove the null hypothesis is true.

Key Concepts

Null Hypothesis

The null hypothesis is a statement that there is no effect or no difference in a population, serving as the default assumption in hypothesis testing. It is tested against an alternative hypothesis to determine if there is enough evidence to reject it.

Role of Sample Evidence in Hypothesis Testing

Sample evidence is used to assess the plausibility of the null hypothesis by calculating the probability of observing the data if the null is true. It can provide evidence to reject the null but cannot definitively prove it true.

Concept of Falsifiability and Proof in Statistics

In statistics, hypotheses are tested by attempting to falsify the null hypothesis. Failure to reject the null does not prove it true; it only indicates insufficient evidence against it, highlighting the asymmetry between disproving and proving hypotheses.