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11 June, 15:23

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?

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  1. 11 June, 15:52
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    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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