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

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