When observed results are unlikely under the assumption that the null hypothesis is true, we say the result is _____and we reject the null hypothesis.

Verified step by step guidance

1. Understand the context: In hypothesis testing, we start with a null hypothesis (H0) which represents a default or no-effect assumption.
2. Recognize that when the observed data is very unlikely assuming the null hypothesis is true, it suggests that the null hypothesis may not be correct.
3. This unlikeliness is quantified by the p-value, which measures the probability of observing data as extreme as, or more extreme than, the actual observed results under the null hypothesis.
4. If the p-value is less than a predetermined significance level (commonly denoted as \( \alpha \), such as 0.05), the observed result is considered statistically significant.
5. Therefore, when the observed results are unlikely under the null hypothesis, we say the result is \textbf{statistically significant} and we reject the null hypothesis.

Key Concepts

Null Hypothesis

The null hypothesis is a default assumption that there is no effect or difference in a study. It serves as a baseline for statistical testing, and researchers seek evidence to determine whether to reject or fail to reject it.

Statistical Significance

Statistical significance indicates that observed results are unlikely to have occurred by random chance alone, given the null hypothesis is true. It is often determined by a p-value threshold, commonly 0.05.

Rejecting the Null Hypothesis

Rejecting the null hypothesis means concluding that the observed data provide sufficient evidence to support an alternative explanation. This decision is made when results are statistically significant and unlikely under the null.