shootingstar

Sasankm, you are correct and I think you have got your sampling concepts good. In my first reading, I was no where close to your level of understanding.

Now, for clarification on your query, you need to understand 2 basic applications of Sampling Techniques:

1. When Mean of the Population is known: Example for this could be, say a machine which produces a job with a Mean length of 2.5 cm (This is the known population mean). A quality manager takes a daily sample of outputs and based on the Mean of that sample, he/she has to decide whether or not to fix/tune the machine. In this case, you have your sample mean for the day and you need to see how many Standard Deviations (SD of distribution of sample means) is your Sample Mean away from actual Population Mean, for a given confidence level. If it fits in, you dont have to tune your machine and if not then you require tuning of your machine. So, this could be the type of application, when you do know your Population Mean.

2. When Mean of the Population is Not Known: This is the case, when you are using a sample to get its mean and estimating that for Population Mean. This you are doing because, calculating the Mean for entire population is either not affordable or not feasable. In this case, you are taking/using sample mean as Population Mean. But you need to document this in your research, so that your audience knows the possibility and extent of error in assuming Sample Mean as Population Mean.

Also, in both the above cases, Population SD may or may not be known. If Population SD is not known, you will use SD of your sample to get SD for the distribution of sample means and use t-test instead of z-test for any further analysis of the case.

Hope this helps.