The p-value is used to assess whether the slope coefficient is equal to zero, which is the null hypothesis. The null hypothesis can be rejected at this level of significance, which is the lowest value. By comparing the p-value to the specified significance threshold to determine whether a coefficient is significant, we may determine whether the null hypothesis can be ruled out.
The null hypothesis can be rejected if the p-value is less than the significance level.
The null hypothesis cannot be rejected if the p-value exceeds the significance level.
Let’s say we want to test whether a new weight-loss drug is effective. We randomly select two groups of overweight individuals: one group takes the drug, while the other takes a placebo. We measure the weight loss in both groups after 12 weeks and calculate the difference in means.
We want to test whether the difference in means is statistically significant, so we conduct a two-sample t-test with a significance level of 0.05. We obtain a t-statistic of 2.5 and calculate a corresponding p-value of 0.015.
This p-value means that there is a 1.5% chance of observing a difference in means as extreme as, or more extreme than, the one we calculated, assuming that the null hypothesis (that there is no significant difference between the two groups) is true. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the weight-loss drug is effective.