Answer:
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
[tex]S^2_c = \frac{S^2_1(n_1-1)+S^2_2(n_1-1)}{(n_1-1)+(n_2-1)}[/tex]
Where:
S[tex]_c[/tex]² = 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
[tex]S^2_c = \frac{10^2(8-1)+8^2(8-1)}{(8-1)+(8-1)}[/tex]
S[tex]_c[/tex]² = 82
The variance of the difference between the two mean is;
[tex]S^2_{(\bar {x}_1-\bar {x}_1)} = \frac{S^2_c}{n_1}+\frac{S^2_c}{n_2} =2\times \frac{82}{8}[/tex] = 20.5
Therefore the standard deviation of the difference is √20.5 = 4.53.
