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Introduction

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter.
Because of their random nature, it is unlikely that two samples from a particular population will yield identical confidence intervals.
But if you repeated your sample many times, a certain percentage of the resulting confidence intervals would contain the unknown population parameter.

Statistical inference is of two types :-
a) Hypothesis testing
b) Estimation

Estimation is point and interval (but we are mainly talking about interval)

Difference in terms of the explicit hypothesis

It is the same underlying math. when H0 : μ0;
z = 𝓍-μ / (𝜎/√n)

Different ways of conceptualizing :

If we were to repeatedly take identical samples (same size) and build similar CI bounds for each sample then 95% of such CI bounds will cover the true mean.

We are 95% confident/certain that the true mean is within our confidence interval.

Examples and Formulas