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The mean height of a sample of 15-year-old boys is 175 centimeters, with a standard deviation of 10. For a sample of 15-year-old girls, the mean is 165 centimeters with a standard deviation of 8.

If 8 boys and 8 girls were sampled, the standard deviation of the difference is

. (Round your answer to the nearest hundredth.)

The standard deviation of the difference is 4.53

Step-by-step explanation:

Here we have the formula for the combined estimate of the variance given as

Where:

S² = Combined variance

n₁ = Sample size of the sample of boys = 8

n₂ = Sample size of the sample of girls = 8

S₁² = Variance of the first sample of boys = 10²

S₂² = Variance of the second sample of girls = 8²

Therefore we have

S² = 82

The variance of the difference between the two mean is;

= 20.5

Therefore the standard deviation of the difference is √20.5 = 4.53.

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