Given:
The standard deviation are given as,
[tex]\begin{gathered} \sigma_{m_1}=\text{ 3.868} \\ \sigma_{m_2}\text{ = 2.933} \\ \end{gathered}[/tex]Required:
The standard deviation of the sample mean differences.
Explanation:
The formula for the deviation of the sample mean difference is given as,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}} \\ \end{gathered}[/tex]Substituting the values in the above formula,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{3.868^2}{n_1}+\frac{2.933^2}{n_2}} \\ \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{14.9614}{n_1}+\frac{8.6025}{n_2}} \end{gathered}[/tex]Answer:
Thus the required answer is,
[tex]\sigma_{m_1}-\text{\sigma}_{m_2}=\sqrt{\frac{\text{14.9614}}{n_1}+\frac{\text{8.6025}}{n_2}}[/tex]
