Question

Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.)
  

	Standard Error
(a) σ = 12, n = 4	Not attempted
(b) σ = 12, n = 16	Not attempted
(c) σ = 12, n = 64	Not attempted

Answer 1

The standard error of the mean is the standard deviation of the sampling distribution of the mean. It is, therefore, the square root of the variance of the sampling distribution of the mean and can be written as:

OM IN

The standard error is represented by a σ because it is a standard deviation. The subscript (M) indicates that the standard error in question is the standard error of the mean.

Now we will get the standard error for the following situations:

(a) σ_M = 12/√4 = 6

(b) σ_M = 12/√16 = 3

(c) σ_M = 12/√64 = 1.5

Hence from here, we can conclude that the standard error is decreasing on increasing number of Sample.

Hope this explanation has helped you.

Thanks!!