Question

Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.Sample Standard Deviationred box 3.868blue box 2.933

Answer 1

Given:

The standard deviation are given as,

`\begin{gathered} \sigma_(m_1)=\text{ 3.868} \\ \sigma_(m_2)\text{ = 2.933} \\ \end{gathered}`

Required:

The standard deviation of the sample mean differences.

Step-by-step explanation:

The formula for the deviation of the sample mean difference is given as,

`\begin{gathered} \sigma_(m_1)-\text{ }\sigma_(m_2)\text{ = }\sqrt{(\sigma_1^2)/(n_1)+(\sigma_2^2)/(n_2)} \\ \end{gathered}`

Substituting the values in the above formula,

`\begin{gathered} \sigma_(m_1)-\text{ }\sigma_(m_2)\text{ = }\sqrt{(3.868^2)/(n_1)+(2.933^2)/(n_2)} \\ \sigma_(m_1)-\text{ }\sigma_(m_2)\text{ = }\sqrt{(14.9614)/(n_1)+(8.6025)/(n_2)} \end{gathered}`

Answer:

Thus the required answer is,

`\sigma_(m_1)-\text{\sigma}_(m_2)=\sqrt{\frac{\text{14.9614}}{n_1}+\frac{\text{8.6025}}{n_2}}`