The standard deviation of a sample taken from population A is 17.6 for a sample of 25. The standard deviation of a sample taken from population B is 21.2 for a sample of 30. The standard deviation of the sample mean difference is?

The answer is 5.5

The standard deviation (sd or σ) of the sample mean difference is:

sd = √ (sd₁²/n₁ + sd₂²/n₂)

For the population A:

sd₁ = 17.6

n₁ = 25

For the population B:

sd₂ = 21.2

n₂ = 30

Hence:

sd = √ (sd₁²/n₁ + sd₂²/n₂)

= √ (17.6²/20 + 21.2²/30)

= √ (309.76/20 + 449.44/30)

= √ (15.49 + 14.98)

= √ (30.47)

= 5.5