Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Answer 1

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

$S^2_c = \frac{S^2_1(n_1-1)+S^2_2(n_1-1)}{(n_1-1)+(n_2-1)}$

Where:

S$_c$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

$S^2_c = \frac{10^2(8-1)+8^2(8-1)}{(8-1)+(8-1)}$  

S$_c$² = 82

The variance of the difference between the two mean is;

$S^2_{(\bar {x}_1-\bar {x}_1)} = \frac{S^2_c}{n_1}+\frac{S^2_c}{n_2} =2\times \frac{82}{8}$ = 20.5

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