Question

Please provide one or more real-world examples for use of confidence interval estimation (include sample size determination), along with a brief description of the test methodology or analysis methodology.

Answer 1

Let us consider a real problema:

You want to find the confidence interval for population, where your aim is to find the say 95% confidence interval for life expectany of that population.

suppose that you find the C.I.(confidence interva) in this case is [X_1, X₂] ; where X₁< X₂

Now lets talk about sample size determination, sample size determination is the key to find an appropriate confidence interval, if you took less samples than you accuracy of C.I. will decrease and If you took sample size more than it will costly.

So determining the sample is very important, we have different differenr formulae for different different distributions.

Hence this(sample size determination) is completely based upon which disrtibution you are taking.

Testing Methodology:

Testing methodology is basically testing the hypotheis, nothing more;

in this you need to set H₀: Null Hypothesis (Which likely to rejected) against H₁: Alternative hypothesis.

If alpha is lesser than p - Value then we go with  H₁: Alternative hypothesis. Otherwise we are not able to reject H₀

Cheers!!