Null Hypothesis vs P-Value
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Null hypothesis
Hypothesis testing
The null hypothesis, written H0, is the default claim of no effect or no difference, assumed true unless the sample data give strong evidence against it.
The null hypothesis, written (read H-naught), is the skeptical starting point that nothing unusual is going on. It always contains an equals sign, fixing the parameter at one value so the test can build a sampling distribution around it. For example, testing a new teaching method against the old one uses , the claim of no improvement. A test never proves ; it either rejects it or fails to reject it for lack of evidence.
P-value
Hypothesis testing
A p-value is the probability, computed assuming the null hypothesis is true, of getting a result at least as extreme as the one you observed.
A p-value measures how well your data agree with the null hypothesis: a small p-value means the observed result would be surprising if the null were true, which counts as evidence against it. It is a probability about the data, not the probability that the null hypothesis is true. For example, a p-value of 0.02 says that if the null hypothesis held, data at least this extreme would occur about 2% of the time. You reject the null hypothesis when the p-value is at or below the significance level (the Greek letter alpha).