Applications of Standard Error

1. Standard Error is used to test whether the difference between the sample statistic and the population parameter is significant or is due to sampling fluctuations.

2. Standard Error is used to find the precision of the sample estimate of a population parameter. If a statistic θ is used to estimate the parameter, then precision of θ = 

3.   It is used to find the interval estimate of a population parameter

Example 

A population consists of four numbers 3, 4, 2, 5. Consider all possible distinct samples of size two and verify that the population mean is equal to the mean of the sample means.

The population mean (μ) = (3 + 4 + 2 + 5) / 4 = 3.5

All possible distinct samples of size two and the corresponding sample means are shown in the following table.

Samples of Size Two and their Sample Means

[Sampling used in the above table is random sampling without replacement and the no. of samples = ⁴C₂ = 6].

Mean of sample means = 21.0/6 = 3.5

Hence, the population mean = 3.5 = the mean of the sample means.