Question

A fourth grade class of 28 students is given a standardized math test. The mean score of the 12 boys is 25 with a standard deviation of 3. The mean score of the 16 girls is 24 with a standard deviation of 4. What is the standard error for the sampling distribution

Answer 1

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:

$\bar x=24\\s_{x}=4\\n_{x}=16\\\bar y=25\\s_{y}=3\\n_{y}=12$

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:

$S_{p}=\sqrt{\frac{s_{x}^{2}}{n_{x}^{2}}+\frac{s_{y}^{2}}{n_{y}^{2}}}$

Compute the standard error for the sampling distribution as follows:

$SE=\sqrt{\frac{s_{x}^{2}}{n_{x}^{2}}+\frac{s_{y}^{2}}{n_{y}^{2}}}=\sqrt{\frac{4^{2}}{16}+\frac{3^{2}}{12}}=\sqrt{1+\frac{9}{12}}=\sqrt{\frac{21}{12}}=1.323$

Thus, the standard error for the sampling distribution is 1.323.