Inference for proportions
A sample found that some share of people have a feature. What does that say about the share in the whole population, or about what a treatment changed?
Where you are 5 inside
What this area is about
A sample proportion \hat{p} is known; the population proportion p is not, and another sample would give another \hat{p}. This area turns one or two sample shares into a range of plausible values for p, or into a verdict on a claimed value. Every procedure here leans on the normal curve, so every one starts by checking when that curve fits.
How these fit together
The groundwork. The conditions for one proportion are three: a random sample, or a randomized experiment using random assignment; n \le 0.10N when sampling without replacement; and large counts, at least 10 successes and 10 failures, checked with \hat{p} for an interval and with the null value p_0 for a test.
One proportion. The one-sample interval estimates p and sizes a survey; the one-sample test checks a claimed p_0.
Two proportions. The interval and the test for a difference of proportions compare two groups, with the conditions checked in each and the two samples independent. The test checks large counts with the pooled proportion, since its null hypothesis says the two shares are equal.
A path through it
The conditions first, then the one-sample interval and test. Next the two-sample interval, then the two-sample test.
Finish here and choosing an inference procedure asks which of these, or of the tests for means, fits a study.