How To Determine Sample Size For Known Population

Formula to Determine Sample Size of Population

Sample Size Formula helps in computing or determining the minimum sample size which is required in order to know the adequate or correct proportion of the population along with the confidence level and the margin of fault.

The term "sample" refers to the portion of the population that enables us to draw inferences well-nigh the population and and then it is important that the sample size is adequate plenty and so that meaningful inferences can exist fabricated. In other words, information technology is the minimum size that is needed to estimate the true population proportion with the required margin of mistake and confidence level. Every bit such, the determination of the appropriate sample size is one of the recurrent problems in statistical assay. Its equation tin can be derived by using population size, the critical value of the normal distribution, sample proportion, and margin of mistake The margin of error is a statistical expression to determine the percentage point the result arrived at will differ from the actual value. Standard deviation divided by the sample size, multiplying the resultant effigy with the critical factor. Margin of Fault = Z * ơ / √n read more .

Sample Size n = Due north * [Z² * p * (1-p)/e²] / [Northward – i + (Z² * p * (1-p)/east²]

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For eg:
Source: Sample Size Formula (wallstreetmojo.com)

where,

N = Population size,
Z = Critical value of the normal distribution at the required confidence level,
p = Sample proportion,
e = Margin of error

How to Calculate Sample Size? (Step by Step)

Footstep one: Firstly, make up one's mind the population size, which is the total number of singled-out entities in your population, and it is denoted by N. [Note: In instance the population size is very large but the exact number is not known, and so employ 100,000 because the sample size doesn't change much for populations larger than that.]
Step 2: Next, determine the critical value of the normal distribution Normal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the eye and few are in the tails, at the extremes. This distribution has two primal parameters: the hateful (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy. read more at the required confidence level. For example, the critical value at 95% conviction level is one.96.
Footstep iii: Next, determine the sample proportion which can be used from previous survey results or be collected by running a modest airplane pilot survey. [Note: if unsure, i tin can always use 0.5 as a bourgeois approach, and it volition give the largest possible sample size.]
Footstep 4: Side by side, determine the margin of error, which is the range in which the true population is expected to lie. [Note: Smaller the margin of mistake, more is the precision and hence the exact answer.]
Step 5: Finally, the sample size equation can exist derived by using population size (step 1), the critical value of the normal distribution at the required confidence level (step ii), sample proportion (step 3), and margin of mistake (pace iv) every bit shown beneath.

Examples

You tin download this Sample Size Formula Excel Template here – Sample Size Formula Excel Template

Example #1

Permit u.s. take the example of a retailer who is interested to know how many of their customers bought an item from them after viewing their website on a sure 24-hour interval. Given that their website has on average, 10,000 views per day determine the sample size of the customers that they have to monitor at a 95% confidence level with a v% margin of error if:

They are uncertain of the electric current conversion rate.
They know from previous surveys that the conversion rate is five%.

Given,

Population size, N = 10,000
Critical value at 95% confidence level, Z = 1.96
Margin of error, eastward = 5% or 0.05

1 – Since the current conversion rate is unknown, let united states assume p = 0.five

Therefore, the sample size can be calculated using the formula as,

= (10,000 * (i.96 ²)*0.5*(1-0.five)/(0.05 ²)/(10000 – i+((1.96 ^two)* 0.5*(ane-0.5)/(0.05 ²))))

Therefore, 370 customers will exist adequate for deriving meaningful inference.

ii – The electric current conversion rate is p = 5% or 0.05

Therefore, the sample size can be calculated using the above formula as,

= (10,000 * (1.96 ⁱⁱ)*0.05*(ane-0.05)/(0.05 ²)/(10000 – 1+((1.96 ²)* 0.05*(1-0.05)/(0.05 ²))))

Therefore, a size of 72 customers volition exist acceptable for deriving meaningful inference in this case.

Instance #ii

Let the states have the above case, and in this case, allow us presume that the population size, i.eastward., daily website view, is between 100,000 and 120,000, simply then the exact value is not known. The rest of the values are the same, along with a conversion charge per unit of five%. Calculate the sample size for both 100,000 and 120,000.

Given,

Sample proportion, p = 0.05
Critical value at 95% confidence level, Z = 1.96
Margin of error, e = 0.05

Therefore, the sample size for N = 100,000 can be calculated as,

= (100000 * (1.96 ⁱⁱ)*0.05*(1-0.05)/(0.05 ²)/(100000 – 1+((1.96 ²)* 0.05*(1-0.05)/(0.05 ^two))))

Therefore, the sample size for Due north = 120,000 tin be calculated as,

= (120000 * (1.96 ²)*0.05*(ane-0.05)/(0.05 ^two)/(120000 – 1+((1.96 ²)* 0.05*(1-0.05)/(0.05 ²))))

Therefore, it is proved that as the population size increases to be very big, information technology becomes irrelevant in the computation of the sample size.

Relevance and Uses

Sample size adding is important to understand the concept of the advisable sample size because information technology is used for the validity of research findings. In instance it is likewise small, it will non yield valid results, while a sample is too large may exist a waste of both money and time. Statistically, the significant sample size is predominantly used for market inquiry surveys, healthcare surveys, and education surveys.

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