Answer:
The standard error for the sampling distribution is 1.323.
Step-by-step explanation:
Let X = scores of girls and Y = scores of boys.
The information provided is:
[tex]\bar x=24\\s_{x}=4\\n_{x}=16\\\bar y=25\\s_{y}=3\\n_{y}=12[/tex]
As the population standard deviations are not known, use a pooled standard deviation to estimate the standard error of the sampling distribution.
The formula of pooled standard deviation is:
[tex]S_{p}=\sqrt{\frac{s_{x}^{2}}{n_{x}^{2}}+\frac{s_{y}^{2}}{n_{y}^{2}}}[/tex]
Compute the standard error for the sampling distribution as follows:
[tex]SE=\sqrt{\frac{s_{x}^{2}}{n_{x}^{2}}+\frac{s_{y}^{2}}{n_{y}^{2}}}=\sqrt{\frac{4^{2}}{16}+\frac{3^{2}}{12}}=\sqrt{1+\frac{9}{12}}=\sqrt{\frac{21}{12}}=1.323[/tex]
Thus, the standard error for the sampling distribution is 1.323.
