The number of people included in a research study to reflect a population is referred to as sample size in research. The overall number of respondents included in a study is referred to as the sample size, and this number is generally split down into sub-groups based on demographics such as age, gender, and geography to ensure that the total sample accurately represents the entire population. One of the most crucial aspects of statistical analysis is determining the optimum sample size. If the sample size is too small, the results will be invalid and the population being investigated will not be appropriately represented. Larger sample sizes, on the other hand, give reduced margins of error and are more representative, but an excessively high sample size can considerably increase the cost and time required to perform the research.

What is the significance of determining the sample size?

Are you prepared to conduct a survey of your study subjects? You can use research surveys to learn more about your target audience. The information you gather allows you to better address the demands of your customers, resulting in higher sales and client loyalty. The researcher must calculate and decide sample size in order to identify the appropriate number of respondents while keeping the research study's quality in mind.
So, how do you figure out the sample size? What criteria do you use to determine who should receive your survey? What factors do you consider when determining the size of your target audience?
Sending out an excessive number of surveys can be costly without providing a clear advantage over a smaller sample. You won't have enough data to draw correct conclusions if you send out too few surveys. Knowing how to effectively calculate and estimate sample size can provide you a competitive advantage. Let's have a look at what constitutes a decent sample. Let's also have a look at the sample size calculation formula so you can figure out the ideal sample size for your next survey.

What is the purpose of determining sample size?

Assume you're a Nigerian market researcher who wants to send out a survey or questionnaire. The goal of the poll is to learn how your target audience feels about a new cell phone you're planning to release. You want to know what Nigerians think about the new product so you can anticipate whether it will be a success or a failure before it is released.
Assume you chose Lagos, which has a population of 40 million people. You choose a sample of 500 people who fit the consumer panel criterion using a sample size determination formula. The responses can be used to predict how your target audience will react to the new product.
Knowing how to calculate a sample size, on the other hand, necessitates more than merely distributing your survey to as many individuals as possible. If you use an excessively large sample size, you risk wasting resources, time, and money. A tiny sample size prevents you from getting the most out of your data, resulting in inconclusive conclusions.

What are the different words for sample size?

Let's have a look at some words you should be familiar with before we get into sample size determination:
The population size: The population size refers to the number of persons who fit your demographic. For example, suppose you're looking for information on doctors in Nigeria. The total number of doctors in Nigeria is your population size. Don't be concerned! It is not always necessary to have a large population. If you know who you're aiming to portray, a smaller population size can still offer you accurate findings.
Confidence level: This metric indicates how confident you can be that your data is correct. It is expressed as a percentage with the confidence interval aligned. If your confidence level is 90%, for example, your results will almost certainly be 90% accurate.
The confidence interval (margin of error): There's no way to be 100 percent accurate when it comes to surveys. Confidence intervals indicate how far you're ready to allow your data to deviate from the population mean. A margin of error is a measure of how near a survey result can be expected to be to the true population value. Remember to utilize our margin of error calculator if you need assistance with this information.
Standard deviation: A data set's dispersion from its mean is measured by standard deviation. It calculates a distribution's absolute variability. The standard deviation and degree of the deviation increase as the dispersion or variability increases. You've already sent out your survey, for example. What level of variation do you anticipate in your responses? The standard deviation is the amount of variation in a response.
Sample size calculation formula – Learn how to calculate your sample size Using the Taro Yamane Formular

Taro Yamane, a mathematical statistician, devised a formula for estimating or determining sample size in respect to the population under study, allowing inferences and conclusions drawn from the survey to be applied to the complete population from which the sample was drawn.

Most researchers or project students struggle to determine the appropriate sample size for their project, research, or survey work during their investigation. Before questionnaires are written and sent out into the field to collect data for analysis, sample sizes must be determined. Because the conclusions gained from the uncalculated sample size would not be precise enough in making a decision on the hypothesis under examination, project managers may decide to cancel the research/project work completely.
The purpose of calculating sample sizes correctly is to ensure that the conclusions gained after analysis can be applied to the full population under investigation.
As a result of our passion for research, we've decided to teach students and researchers how to calculate sample size for their projects and research papers in the most reliable and effective method possible. One of the most widely used methods for calculating sample size is shown below.
The statistical formula devised by Taro Yamane is as follows:
n = N/ 1+ N(e)2
In the formular above;
n is the required sample size from the population under study
N is the whole population that is under study
e is the precision or sampling error which is usually 0.10,0.05 or 0.01
Example:
Using the Taro Yamane’s statistical formular to determine the adequate sample size of say 300 respondents under study. This would hence be

n = N/ 1+ N(e)2
N=300; e= 0.1; e2= 0.01
n = 300/1+ 300(0.1)2
n= 100.
Therefore, a sample size 100 respondents out of the entire population of 300 respondents would therefore be the lowest acceptable number of responses to maintain a 95% confidence level.

Brilliant,
Please what if your population is much larger which of the 'e' is more appropriate to use (0.5, 0.10 or 0.1)

And I will like to know how you punch your calculator to arrive at 100 from your example?