Confidence intervals
One random sample gives one estimate, almost surely a little off. How do you report a range that honestly says how far off it might be?
Where you are 4 inside
What this area is about
A confidence interval reports an estimate from a random sample together with a distance: \text{point estimate} \pm \text{margin of error}. The values inside are the plausible values of the parameter in light of that sample. Its percent, the confidence level, belongs to the method, not to one computed interval: it is the share of all possible random samples for which the method would capture the parameter. The margin of error covers only the chance variation of random sampling, not bias from a poorly drawn sample.
How these fit together
Building blocks. Standard error estimates the spread of a statistic’s sampling distribution from the sample itself, such as \displaystyle \text{SE}_{\hat{p}} = \sqrt{\hat{p}(1 - \hat{p})/n}. Point estimates and the margin of error multiply it: \text{ME} = (\text{multiplier}) \times \text{SE}.
Meaning. Confidence level and interpreting an interval says what the percent is a statement about, and what a report may honestly claim from one interval.
Precision. Critical value gives the exact multiplier z^* for any chosen level, when the statistic’s sampling distribution is close to normal.
A path through it
Standard error, then margin of error, then confidence level, then critical value.
Finish here and you can build a one-sample z interval for a proportion and a one-sample t interval for a mean.