The standard deviation of a mean difference = 5.23
Explanation:Given:
Standard deviation of a sample taken from population A = 17.6
the number of samples = 25
Standard deviation of a sample taken from population B = 21.1
the number of samples = 30
To find:
the standard deviation of the mean difference
The standard deviation of a mean difference is given as:
[tex]\begin{gathered} \sigma\text{ = }\sqrt{\frac{\sigma_{A^2}}{n_A}+\frac{\sigma_B^2}{n_B}} \\ \sigma\text{ = standard deviation of the sample mean difference} \end{gathered}[/tex][tex]\begin{gathered} \sigma\text{ = }\sqrt{\frac{17.6^2}{25}+\frac{21.2^2}{30}} \\ \\ \sigma\text{ = }\sqrt{12.3904+14.9813} \\ \\ \sigma\text{ = }\sqrt{27.3717} \\ \\ \sigma\text{ = 5.23} \end{gathered}[/tex]The standard deviation of a mean difference = 5.23
