Sampling Error Formula
Sampling error technique is employed to compute the total selection bias in statistical analysis, as the name implies. To refresh your memory, sampling error is a statistical mistake caused by the nature of sampling. The atypical-ness of the observations in the samples collected causes statistical analysis errors.
Because sampling is used to identify the characteristics of a full population, the discrepancy between the sample values and the population is referred to as sampling error. It’s important to remember that calculating the precise value of sampling is impossible because the population value is unknown, yet sampling error may typically be calculated using statistical models of a sample.
Sampling Error Formula
SE = Z x σ/√n
where,
- Z denotes the score value
- σ refers to the population standard deviation
- n is the sample size
Sample Problems on Sampling Error
Question 1. Find the sampling error at a 95% confidence level given the standard deviation of the population is 0.23 and the sample size is 2145.
Solution:
Given: Z = 95%, σ = 0.23 and n = 2145
Since, SE = Z x σ/√n
= 1.96 x (0.23/√2145)
= 1.96 x 0.00496608
SE = 0.009733
Question 2. Find the sampling error at a 90% confidence level given the standard deviation of the population is 0.2 and the sample size is 100.
Solution:
Given: Z = 92%, σ = 0.2 and n = 100
Since, SE = Z x σ/√n
= 1.645 x (0.2/√100)
= 1.645 x 0.02
SE = 0.0329
Question 3. Find the sampling error at a 99% confidence level given the standard deviation of the population is 0.2 and the sample size is 36.
Solution:
Given: Z = 99%, σ = 0.2 and n = 100
Since, SE = Z x σ/√n
= 2.58 x (0.2/√36)
= 2.58 x 0.0333
SE = 0.085914
Question 4. Find the sampling error at a 99% confidence level given the standard deviation of the population is 0.9 and the sample size is 49.
Solution:
Given: Z = 99%, σ = 0.9 and n = 49
Since, SE = Z x σ/√n
= 2.58 x (0.9/√49)
= 2.58 x 0.1285
SE = 0.33153
Question 5. Find the sampling error at a 95% confidence level given the standard deviation of the population is 0.3 and the sample size is 81.
Solution:
Given: Z = 95%, σ = 0.3 and n = 81
Since, SE = Z x σ/√n
= 1.96 x (0.3/√81)
= 1.96 x 0.03333
SE = 0.0653268
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