Formula to Calculate Sampling Error

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Where,

  • Z is the Z score value based on the confidence intervalσ is the population standard deviationn is the size of the sample

Step by Step Calculation of Sampling Error

Examples

Example #1

Suppose the population standard deviation is 0.30 and the sample size is 100. What will the sampling error be at a 95% confidence level?

  • Gathered all sets of data called the population. Compute the population means and population standard deviation. Now, one needs to determine the sample size. Further, the sample size has to be less than the population and should not be greater. Determine the confidence level. Accordingly, one can determine the value of the Z-score from its table. Now, multiply the Z-score by the population standard deviation and divide the same by the square root of the sample size to arrive at a margin of error or sample sizeSample SizeThe sample size formula depicts the relevant population range on which an experiment or survey is conducted. It is measured using the population size, the critical value of normal distribution at the required confidence level, sample proportion and margin of error.read more error.

Solution

Here, we have given the population standard deviation as well as the size of the sample. Therefore, we can use the below formula to calculate the same.

Use the following data for the calculation.

  • Z Factor Value: 1.96The population of standard deviation: 0.3Sample Size: 100

Therefore, the calculation of the sampling error is as follows,

Sampling Error will be –

Example #2

Gautam is currently pursuing an accountancy course and has cleared his entrance exam. He has registered now for an intermediate level and will also join a senior accountant as an intern. In addition, he will be working on an audit of the manufacturing firms. 

One of the firms he was visiting for the first time asked to check whether the bills for all the purchase entries were reasonably available. The sample size he picked was 50, and the population standard deviation for the same was 0.50.

Based on available information, you must calculate sampling error at 95% and 99% confidence intervals.

Here we are given the population standard deviation as well as the size of the sample; therefore, we can use the below formula to calculate the same.

Z-score for a 95% confidence level will be 1.96 (available from the Z-score table)

  • Z Factor Value: 1.96The population of standard deviation: 0.50Sample Size: 50

Therefore, the calculation is as follows,

Z score for 95% confidence level will be 2.58 (available from Z score table)

As the confidence level increases, the sampling error also increases.

Example #3

In a school, a biometric session was organized to check the students’ health. They initiated the session with students of class X standard. In total, there are 30 students in the B division. Among them, 12 students were selected randomly for a detailed checkup, and the rest were only basic tests. The report inferred that the average height of the students in the B division is 154.

The population standard deviation was 9.39. You must calculate a 90% and 95% confidence interval sampling error based on the above information.

Here, we have the population standard deviation as well as the size of the sample. Therefore, we can use the below formula to compute the same.

The 95% confidence level Z-score will be 1.96 (available from the Z-score table).

Z score for 90% confidence level will be 1.645 (available from Z score table)

As the confidence level decreases, the sampling error also decreases.

Relevance and Uses

It is vital to understand this concept as it shall depict how much one can expect the survey results to depict the overall view of the population. One needs to remember a survey uses a smaller population called the sample size (also known as the survey respondents) to represent a bigger population.

One can view it as a way of calculating the effectiveness of the survey. When the sampling margin is higher, it shall represent that the survey consequences might stray from the actual total population representation. On the flip side, a sampling error or margin of errorMargin Of ErrorThe 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 figure with the critical factor. Margin of Error = Z * ơ / √nread more that is smaller than that shall indicate that the consequences are now closer to the true representation of the population in total and which shall build a higher level of confidence about the survey under view.

This article has been a guide to the Sampling Error Formula. Here, we discuss the formula to calculate the sampling error along with examples and a downloadable Excel template. You can learn more about accounting from the following articles: –

  • Systematic SamplingSystematic SamplingSystematic sampling is a method of selecting various elements ordered from a sampling frame. This statistical procedure begins with a random selection of elements from a list, and then selects each sampling interval from the frame.read moreSimple Random SamplingSimple Random SamplingSimple random sampling is a process in which each article or object in a population has an equal chance of being selected, and using this model reduces the possibility of bias towards specific objects.read moreFormula of Confidence IntervalFormula Of Confidence IntervalConfidence Interval refers to the degree of uncertainty associated with specific statistics & it is often employed along with the Margin of Error. Confidence Interval = Mean of Sample ± Critical Factor × Standard Deviation of Sample. read moreFormula of Midrange