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POST TITLE:** HOW TO CALCULATE RELIABLE SAMPLE SIZE FOR UNKNOWN POPULATION USING Z SCORE**

Determination of sample size over the history of research project writing has been one of the most important tools for effective data analysis. There are so many ways to determine sample size. The most common method used by research project students who want to engage project writing is the Taro Yamane formula for known population. But in this article I will focus on the determination of reliable sample size for unknown population. The sample size is usually required for project topics under social sciences that involved primary data.

When I say primary data I mean raw data gotten from a particular source; here the primary data are gotten directly from the responses of the respondents either through the use of questionnaires or interview. In the next article I will show undergraduate project students and post graduate project students on how to form questionnaires for different kind of responses.

Before I explain how to use the z score for the determination of reliable sample size for unknown population let me first of all explain the z score. A Z-score is a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

The Z score can be used to determine the reliable sample size by considering normal derivation set at 95% confidence level (1.96). Then we pick a choice or response (50%=0.5) and the confidence interval (0.05 = ± 5) using the formula below:

n = Z2 (P) (1-P)/C2

Where

Z= standard normal deviation set at 95% confidence level

P = percentage picking a choice or response

C= confidence interval

n = (1.96)2 (0.5) (1-0.5)/ (0.05)2

n = (3.8416)(0.5)(0.5)/0.0025

n = 0.9604/0.0025

n ≈ 384.16

n = 384

The sample size for the study will be 384. The sample size can still change depending on what confidence level you want to choose. An undergraduate project student can practice this method trying different confidence level.

The formula is flexible; when you already have the sample size, you can determine the standard normal deviation set at 95% confidence level and also the p-value which is the percentage picking or choice of response. The same goes to finding the confidence interval.