Question

Suppose a simple random sample of size n is drawn from a large population with mean muμ and standard deviation sigmaσ. The sampling distribution of x overbarx has mean mu Subscript x overbarμxequals=​______ and standard deviation sigma Subscript x overbarσxequals=​______.

Answer 1

a.) The Mean mu Subscript x overbarμxequals= μ

b.) The standard deviation sigma Subscript x overbarσxequals= σ overbar square root of n.

Therefore the sample mean is equal to the population​ mean, but the standard error of the mean on the other hand depends on the sample size.

We notice also, that as n​ increases, sigma x over barσx reduces. Therefore n is inversely proportional to sigma x barσx.