Hello Shoki

1. the sample size cannot be fixed in advance for any new problem.

2. The research studies in an field are usually carried out on sample of subjects rather than whole populations. The most challenging aspect of fieldwork is drawing a random sample from the target population to which the results of the study would be generalized.

3. The key to a good sample is that it has to be typical of the population from which it is drawn. When the information from a sample is not typical of that in the population in a systematic way, we say that error has occurred. In actual practice, the task is so difficult that several types of errors, i.e. sampling error, non-sampling error, Response error, Processing error,…

4. In addition, the most important error is the Sampling error, which is statistically defined as the error caused by observing a sample instead of the whole population. The underlying principle that must be followed if we are to have any hope of making inferences from a sample to a population is that the sample be representative of that population.

5. A key way of achieving this is through the use of “randomization”. There several types of random samples, Some of which are: Simple Random Sampling, Stratified Random Sampling, Double-stage Random Sampling... Moreover, the most important sample is the simple random sample which is a sample selected in such a way that every possible sample of the same size is equally likely to be chosen. In order to reduce the sampling error, the simple random sample technique and a large sample size have to be developed.

6. The following factors are highly affected the sample size and need to be identified:

• Population Size,
• Margin of Error,
• Confidence Level (level of significance) and
• Standard of Deviation.

7.The Cochran's formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population.Cochran’s formula is considered especially appropriate in situations with large populations. A sample of any given size provides more information about a smaller population than a larger one, so there’s a ‘correction’ through which the number given by Cochran’s formula can be reduced if the whole population is relatively small.

8. An expression based on Cochran's formula is given

,n0= (z-score )2 x StdDevx(1-StdDev) / (margin of error)2 .

where error stands for the desired level of precision (i.e. the margin of error).

9. If the population we’re studying is small, we can modify the sample size we calculated in the above formula by using this equation,n=((n0/[1+[(n0-1)/N]]).

Regards,

Zuhair

Please refer to:

1. William G. Cochran, Gertrude M. Cox (1977). Experimental Design, Wiley.

2. Snedecor, W.G. and Cochran,W.G. (1989). Statistical Methods, Blackwell.

3.Geoffrey Keppel and Thomas D. Wickens (2004). Design and Analysis: A Researcher's Handbook (4th Edition). International Edition.

Regards

I do agree with Z. A. Al-Hemyari.

As the population if infinite, it is difficult to say that 50 sample size is adequate.

Dear Pantaleon Shoki ,

you should define your population in the first step. then set the problem statement and the research question(s) and your study design. Only after doing these steps you can set/calculate the adequate sample size.

Thanks a lot for you guidance. @Z. A. Al-Hemyari, Dhritikesh Chakrabarty and Marjan Mohammadzadeh

Thanks to Pantaleon Shoki for acknowledging my answer as well as the answers given by Z. A. Al-Hemyari and Marjan Mohammadzadeh.

Best wishes to him.