4.6.A—Calculate the mean and standard deviation of a sampling distribution for the difference between two sample means

Calculate the mean and standard deviation of a sampling distribution for the difference between two sample means.

• For two independent populations with population means µ1 and µ2 and population standard deviations σ1 and σ2, when the sampled values are independent, the sampling distribution of the difference in sample means x12−x has a mean μμ()xx μ 12 12 and standard deviation σσ2 2 σ 1 2 ()xx- =+ 12 nn1 2 .