Dear Gerensea

The minimum sample size estimation depends on the type of your population, is it finite population or infinite population.

In the case of finite population, you can use the attached table to estimate the suitable sample size. Or use Slovin formula:

n= N / ( 1+ N * e^2 ) 

But in the case of an infinite population: 

The sample size for any study depends on the standard deviation of the variable ( from previous studies ) and the margin of error you decided. The formula:

n= ( Z^2 * S^2) / E^2

where : Z  ( 1.96 for 0.05 and 2.58 for 0.01 )

S = standard deviation from previous studies or pilot  study

E = significant level 

Also, you can use software to calculate sample size ( SPSS , Minitab , G*power )

My advice to use G*Power .

G*Power software is an effective tool to calculate sample size for many ranges of experiments. Also, you can determine effect size and power of the test, G*Power is free to download and easy to use after reading the manual, the download link:

http://download.cnet.com/G-Power/3000-2054_4-10647044.html

The link to download G*Power manual:

http://www.gpower.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf

I hope that be useful for you.

Good Luck

The above answer is fine If you want to estimate one population mean with a simple random sample. If your experiment is more complicated, See a book like one of the below for the type of experimental design you want to use. If you are not sure about the design, these books will help you there as well. Best, David

https://www.amazon.com/Biostatistical-Design-Analysis-Using-Practical/dp/1405190086/ref=sr_1_1?ie=UTF8&qid=1489352414&sr=8-1&keywords=murray+logan+biostatistical

https://www.amazon.com/Analysis-Experiments-Chapman-Statistical-Science/dp/1439868131/ref=sr_1_2?ie=UTF8&qid=1489352532&sr=8-2&keywords=John+Lawson

https://www.amazon.com/Biostatistics-Methodology-Health-Sciences-2004-07-26/dp/B01NAN4BRD/ref=sr_1_1?ie=UTF8&qid=1489352984&sr=8-1&keywords=fisher+van+belle

https://www.amazon.com/Fundamentals-Biostatistics-Bernard-Rosner/dp/130526892X/ref=sr_1_1?s=books&ie=UTF8&qid=1489353239&sr=1-1&keywords=rosner+fundamentals+of+biostatistics

Dear Khalid Hassan,

What are the variables' definition in the finite population formula?

Thanks,

Dear Mohammad

The variable definition not different in finite or infinite population and refer to value vary from individual to another like the weight of the body or the color of the eye.

But if your question about finite population, that refer to limited number individuals population 

Good Luck

Thanks. I was actually asking about the definition of N and e in the first equation.

Thanks again,

Dear Mohammad

Slovin formula:

n= N / ( 1+ N * e^2 )

Where: n = sample size; N = population size; e = the level of precision ( margin of the error). In the biological sciences we use 0.05 and 0.01.

Good Luck

Thanks.

Thanks