Assume H0 mu1 mu2 0 is true What are the three defining ch

Assume H₀: mu₁ - mu₂ = 0 is true. What are the three defining characteristics of the sampling distribution of differences between means?

Solution

The three defining characteristics of the sampling distribution of difference between means is as per central limit theorem.

The mean of the sampling distribution (_x) is equal to the mean of the population ().

The standard error of the sampling distribution (_x) is determined by the standard deviation of the population (), the population size (N), and the sample size (n).

These relationships are shown in the equations below:

_x =      and      _x = [ / sqrt(n) ] * sqrt[ (N - n ) / (N - 1) ]

In the standard error formula, the factor sqrt[ (N - n ) / (N - 1) ] is called the finite population correction or fpc. When the population size is very large relative to the sample size, the fpc is approximately equal to one; and the standard error formula can be approximated by _x = / sqrt(n).

The shape of the distribution of sample mean tends to be normal. It is guaranteed to be normal if population from which sample is selected is normal or if sample size is n=30 or more than that.