Assuming the null hypothesis is true, a p-value in statistics measures the probability of getting a result as or more extreme as the observed one. It helps determine how statistically significant a test is.

• p ≤ 0.01 : strong significance
• 0.01 < p ≤ 0.05 : sigificant
• 0.05 < p ≤ 0.1 : light significance
• p > 0.1 : no significance

\(\alpha\) = significance level

If \(p \leq \alpha\), reject the null hypothesis (\(H_0\)).

If \(p > \alpha\), fail to reject the null hypothesis (\(H_0\)).

You are testing whether a new type of fertilizer affects plant growth. You plant 10 plants and apply the fertilizer to 5 of them, while the other 5 receive no fertilizer (control group). After 4 weeks, you measure the plant heights.

The test gives p-value: 0.07

Since p = 0.07 > α = 0.05, we fail to reject the null hypothesis.

Meaing there isn’t enough evidence to suggest that the fertilizer significantly increases plant growth.

\[ z = \frac{(\bar{x} - \mu_0)}{\frac{\sigma}{\sqrt{n}}} \]

\(\bar{x}\) = Sample mean

\(\mu_0\) = Population mean under the null hypothesis

\(\sigma\) = Population standard deviation

n = sample size

Normal Distribution with Null Hypothesis in Red

Null Hypothesis Mean in Red dashed line

Visual of how change in the mean and standard deviation affect the distribution

• The p-value helps determine if the null hypothesis will be rejected
• A small p-value suggests rejecting null hypothesis
• A large p-value suggests no rejecting null hypothesis