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 of $\overline{x}_{boys}$ - $\overline{x}_{girls}$?
A) 1
B) 1.87
C) 1.75
D) 1.32

Question

Quizplus · Accepted Answer

The standard error for the difference in means is calculated using the formula: $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$, where $s_1$ and $s_2$ are the standard deviations, and $n_1$ and $n_2$ are the sample sizes. Plugging in the values: $\sqrt{\frac{3^2}{12} + \frac{4^2}{16}} = \sqrt{\frac{9}{12} + \frac{16}{16}} = \sqrt{0.75 + 1} = \sqrt{1.75} \approx 1.32$.

A Fourth Grade Class of 28 Students Is Given a Standardized