Applications of Standard Error of Mean:
To determine whether a sample is drawn from same population or not when it's mean is known.
To work out the limits of desired confidence within which the population mean should lie. For example, take fasting blood sugar of 200 lawyers. Suppose mean is 90 mg% and SD = 8 mg%. With 95% confidence limits, fasting blood sugar of lawyer's would be; n = 200, SD = 8; hence SEM = SD/√n=8/√200=8/14.14=0.56. Hence, Mean fasting blood sugar + 2 SEM = 90 + (2 × 0.56) = 91.12 while Mean fasting blood sugar - 2 SEM = 90 - (2 × 0.56) = 88.88. So, confidence limits of fasting blood sugar of lawyer's population are 88.88 to 91.12 mg %. If mean fasting blood sugar of another lawyer is 80, we can say that, he is not from the same population.
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