Final answer:
A result based on a random sample is statistically significant if it is unlikely that this result or similar results would be observed if the null hypothesis is true. The p-value is used to determine statistical significance, with a smaller p-value indicating stronger evidence against the null hypothesis.
Step-by-step explanation:
In statistics, a result based on a random sample is considered statistically significant if it is unlikely that this result or similar results would be observed if the null hypothesis is true. This means that the observed test statistic is very unlikely to happen by chance alone, providing evidence that the null hypothesis is false and should be rejected in favor of the alternative hypothesis.
The p-value is used to determine statistical significance. Generally, a p-value smaller than 0.05 (5 percent) or even smaller than 0.01 (1 percent) is considered statistically significant, indicating strong evidence against the null hypothesis. Rejection of the null hypothesis implies that there is enough evidence to support the alternative hypothesis.