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Sampling Error Formula

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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.

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

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


Last Updated : 10 Jan, 2024
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