Arizona State University (ASU) ECN221 Business Statistics Exam 2 Practice

Statistical significance is typically indicated by a p-value less than the significance level, often set at 0.05 or 0.01 in many studies. When researchers conduct hypothesis testing, they calculate the p-value to determine the probability of observing the data (or something more extreme) given that the null hypothesis is true. If the p-value falls below the predetermined significance level, it suggests that there is strong evidence against the null hypothesis and that the observed effect or relationship is unlikely to have occurred by random chance alone.

In practical terms, this means that a low p-value implies that the results are statistically significant, leading researchers to reject the null hypothesis. Conversely, a p-value greater than the significance level indicates that the evidence is not strong enough to consider the results significant, often leading to a failure to reject the null hypothesis.

In this context, the option mentioning a correlation coefficient greater than 0.5 refers to a specific strength of association rather than a formal test of significance. Furthermore, although a large sample size can increase the power of a statistical test, significance is specifically determined through the relationship of the p-value to the significance level and not merely by sample size alone.