Google is a great tool, but it is necessary to be skeptical and evaluate the provided results. For example, upon searching "standard error of the difference between two means" the first hit is a link to a web page from Keane University where the equation for the standard error of the difference between two means is given as:

Question:

The question is incomplete. It can be found in search engines. However, kindly find the complete question in the attachment below.

Answer / Explanation:

It should be noted that what is being displayed by google is :

Standers Error of Population Means (SEμ₁ - μ₂) = √σ₁² / η₁ + σ₂² / η₂

The equation above gives the standard error for population mean. However, it does not give the standard population error for two sample mean so therefore, we can comfortably say that the equation

(SEμ₁ - μ₂) = √σ₁² / η₁ + σ₂² / η₂ is not wrong.

However, moving forward,

the correct equation for standard error for two sample mean is:

(SEε₁ - ε₂) = √ Sp² ( 1 /  η₁  + 1 /  η₂ )

On stating the above equation, It should be understood that the equation above has given the standard error for two sample mean when the population variance are assumed to be equal thus the standard deviations of the two population are assumed to be equal.

So in conclusion, we can say that the correct statement is that Greek letters are usually used in the equations for population parameters whereas Latin letters are usually used in the equation for sample statistics.

Thus, we can say that Latin letters are usually used in the equations for population parameters,

while Greek letters are usually used in the equation for sample statistics is incorrect.

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