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

Practice Questions – Sampling Error Formula

1. A survey estimates the mean height of students in a school to be 160 cm with a standard deviation of 12 cm. If the sample size is 100 students, calculate the sampling error at a 95% confidence level.

2. In a poll of 400 voters, the proportion of people who favor a new policy is 0.45. Calculate the sampling error for the proportion at a 90% confidence level.

3. A sample of 250 households reports an average monthly electricity bill of $120 with a standard deviation of $15. Determine the sampling error at a 99% confidence level.

4. A researcher surveys 50 students to find the average time spent on homework per week. The mean time reported is 6 hours with a standard deviation of 1.5 hours. Calculate the sampling error at a 95% confidence level.

5. In a study, the mean weight of 200 apples is found to be 150 grams with a standard deviation of 20 grams. Find the sampling error at a 95% confidence level.

6. A random sample of 500 people indicates that 60% of them prefer online shopping. Calculate the sampling error for the proportion at a 95% confidence level.

7. The mean annual salary of a sample of 80 teachers is $50,000 with a standard deviation of $5,000. Determine the sampling error at a 90% confidence level.

8. In a survey, a sample of 150 customers reports a mean satisfaction score of 4.2 out of 5 with a standard deviation of 0.8. Calculate the sampling error at a 95% confidence level.

9. A study finds that the average lifespan of 30 electronic devices is 5 years with a standard deviation of 1 year. Determine the sampling error at a 99% confidence level.

10. A sample of 120 students shows that the average number of books read per year is 10 with a standard deviation of 3 books. Calculate the sampling error at a 95% confidence level.

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FAQs on Sampling Error Formula

How to calculate sampling error?

Sampling error can be calculated using the steps given below:

• Calculate or obtain the standard deviation of the sample data.
• Identify the number of observations in the sample.
• Use the formula: SE = s/√n
• Divide the sample standard deviation by the square root of the sample size to get the sampling error.

What is the formula for the sample error of the mean?

The formula for the sample error of the mean, also known as the standard error of the mean, is:

SE = s/√n

where s is the sample standard deviation and n is the sample size.

What is the in-sample error?

In-sample error refers to the error rate of a model when it is tested on the same data that was used to train the model. It measures how well the model fits the training data.