If your study based on selecting a sample from each sector due to each sector has specific characteristics, ghen each sampling process will be named the stratified sampling. Now, for each sector you will sample your sample by following this link which give you a formula:

https://www.statisticssolutions.com/sample-size-formula/

In case you have a population with a finite number of elements and a sample with a repeat, to calculate the optimal number of elements in the sample, you can use the following formula: n(opt)=(SD^2*k^2)/E

where,

SD - standard deviation of the population,

k - significance coefficient (k = 1.96 for a risk of 0.05 or k=2.58 for a risk of 0.01) and

E - half the width of the confidence interval.

Polapally -

It first depends upon whether you might be using a design-based (probability-of-selection-based), model-assisted design-based, or strictly model-based approach.  For an establishment survey, data are typically highly skewed, and you might be using an unequal probability design, or something involving a model.  In fact, a model can tell you the best unequal probability sampling design to use.  See Särndal, Swensson, and Wretman(1992) below.

There is a lot to consider.

Some example textbooks and then papers to consider, selected to cover the range you need:

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.   

An Introduction to Model-Based Survey Sampling with Applications, 2012, Ray Chambers and Robert Clark,  Oxford Statistical Science Series

Finite Population Sampling and Inference: A Prediction Approach,  2000, Richard Valliant, Alan H. Dorfman, Richard M. Royall,

Wiley Series in Probability and Statistics.  

Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.  

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons.

"The model based (prediction) approach to finite population sampling theory," Institute of Mathematical Statistics Lecture Notes - Monograph Series, Volume 17, 1992, 225-240, Richard M. Royall,

 https://www.researchgate.net/publication/254206607_The_model_based_prediction_approach_to_finite_population_sampling_theory/, 

 https://projecteuclid.org/euclid.lnms/1215458849.     

"Three controversies in the history of survey sampling," Survey Methodology, 12-001-X

Volume 39, Number 2

December 2013, Ken Brewer, KRW 

https://www150.statcan.gc.ca/n1/pub/12-001-x/2013002/article/11883-eng.htm

"Comparison of Model-Based to Design-Based Ratio Estimators," Knaub, 2017, Joint Statistical Meetings, https://www.researchgate.net/publication/319434665_Comparison_of_Model-Based_to_Design-Based_Ratio_Estimators

"Quasi-Cutoff Sampling and the Classical Ratio Estimator - Application to Establishment Surveys for Official Statistics at the US Energy Information Administration - Historical Development," Knaub, 2017, invited presentation at US EIA, https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development

"Projected Variance for the Model-based Classical Ratio Estimator: Estimating Sample Size Requirements," Knaub, 2017, Joint Statistical Meetings, https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements

So, there is much more than a single formula to consider. 

Best wishes - Jim

James R Knaub

Thank you very much James , for spending your valuable time for answering my question.

Kosta Sotiroski

Thnak you Kosta for your contribution.

Safaa Kadhem

Thank you Safaa Kadhem for answering my question. But My study is only relating to one sector only and there are number of companies in it. Hence I asked what is the appropriate sample Size, when the population is finite. I have seen some formulas from Levin book relating to sample size but failing to compute.

Because your are from Statistics.

Thank you in advance for your contribution both in terms of time and knowledge sharing.

Polapally -

In addition to my comments and the references I provided above, there is a basic principle for all finite population sample size requirements investigations.  The methodologies may differ: probability-of-selection-based, model-based, or a combination, with particulars such as stratification, cluster sampling, multi-stage sampling, etc.  And don't forget, when needed, the finite population correction (fpc) factor.  Also, type of data matters (continuous and yes/no proportions). 

But the basis for all such sample size estimation is fairly straightforward.  Please note my responses to https://www.researchgate.net/post/I_need_a_sample_size_finding_article_how_to_calculate_sample_size.  There

 I  noted the basic principle to be as follows:

"You need to get bias [of all kinds] under control, and then the driving factor is variance.  You want to know what sample size goes with the inherent standard deviation to yield a satisfactory standard error."   

Note that for stratification, where overall sample size is important, the stratum population standard deviation is important for each stratum. 

Note that for the model-based approach, sigma, the standard deviation, is for the estimated residuals, or for weighted least squares regression, sigma is for the random factors of the estimated residuals.

But the basic principle, regardless, is

....................

What sample size is needed to go with the inherent standard deviation to achieve a desired standard error? 

....................

That standard error might be used in a confidence interval, or analogously, one might have a prediction interval.  (Hypothesis testing, done properly, might be useful.)  

For more than one variable/question of interest, important ones should each be addressed, and the largest sample size need would determine overall need. 

Cheers - Jim 

PS -  Please note that my sample size estimation paper link given previously is for a paper showing a model-based approach which is analogous to a simple random sampling sample size estimation approach shown in Cochran(1977), Sampling Techniques, Third Edition, Wiley.  The parallels are shown.