When we talk about hypothesis testing in statistics, significance levels are very important. They help us decide if we should reject or keep the null hypothesis.

The significance level is usually written as $\alpha$. A common value for $\alpha$ is 0.05. This means there's a 5% chance that we might say there is an effect when there really isn't one. This mistake is called a Type I error.

Let’s break this down into simpler parts:

1. Null Hypothesis ($H_0$): This is the basic idea that says there is no effect or difference. For example, $H_0$: The new medicine does not change the recovery rate.

2. Alternative Hypothesis ($H_1$): This is what we are trying to prove. For instance, $H_1$: The new medicine improves the recovery rate.

3. P-Value: The p-value tells us how likely it is to get results as extreme as the ones we have, assuming the null hypothesis is true. For example, if the p-value is 0.03, it means there's a 3% chance of getting these results if the null hypothesis is actually true.

If the p-value is less than $\alpha$ (like 0.05), we reject $H_0$. This suggests that the new medication likely has a real effect. On the other hand, if the p-value is greater than $\alpha$, we do not reject $H_0$. This means we don't have enough evidence to support the alternative hypothesis.

In short, significance levels help us understand p-values and guide us in making smart decisions based on what the statistics tell us!