Hypothesis testing
A sample disagrees with a claim. Is the gap too large to blame on the ordinary variation between random samples?
Where you are 6 inside
What this area is about
A hypothesis test starts by assuming a claim about a parameter, then asks how surprising the sample would be if that claim were true. If data at least this extreme would be rare under the claim, that counts as evidence against it. The reasoning holds only when the data come from a random sample, random assignment or a random process, and it measures chance alone: it says nothing about how large or important a difference is, and a decision can still be wrong.
How these fit together
Setting up. Null and alternative hypotheses state the claim H_0 (an equality, such as p = 0.80) and the alternative H_a the study looks for, with <, > or \neq.
Measuring. Test statistic counts how many standard deviations the sample statistic sits from the null value, computed as if H_0 were true.
Deciding. Deciding and concluding from a p-value compares the p-value with a significance level \alpha fixed in advance. Cautions about significance separates “detected” from “large enough to matter”.
Errors. Type I and Type II errors name the two wrong decisions, and power is the chance of rejecting H_0 when the true value is a given alternative.
A path through it
Hypotheses, then the test statistic, then p-values (outside this area). After that, the decision and its cautions on one branch, and the two errors then power on the other.
Finish here and you can run a one-sample z test for a proportion.