# P-value

## What is a P-value?

A P-value is a measure of the evidence against a null hypothesis in a hypothesis test. It represents the probability of observing a test statistic at least as extreme as the one calculated from the sample data, assuming the null hypothesis is true. The P-value is used to determine the statistical significance of the results of a hypothesis test.

## How to interpret a P-value?

A P-value is typically compared to a predetermined significance level (α). If the P-value is less than or equal to α, the null hypothesis is rejected, and the results are considered statistically significant. Commonly used significance levels are 0.05 (5%) and 0.01 (1%). A smaller P-value indicates stronger evidence against the null hypothesis.

## P-value example:

In the T-test example presented above, we computed a P-value using the following code:

``````t_statistic, p_value = ttest_ind(group1, group2)
print("P-value:", p_value)
``````

To determine if the difference between the means of the two groups is statistically significant, we can compare the P-value to a significance level:

``````alpha = 0.05
if p_value <= alpha:
print("Reject the null hypothesis: The means are significantly different.")
else:
print("Fail to reject the null hypothesis: The means are not significantly different.")
``````