Answer: B. 1.679
Step-by-step explanation:
The standard deviation for the difference between two mean is given by :-
[tex]SD_{\overline{x}_1-\overline{x}_2}=\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}[/tex]
, where [tex]n_1[/tex] = sample size from population 1.
[tex]n_2[/tex] = sample size from population 2.
[tex]\overline{x}_1-\overline{x}_2[/tex] = sample mean differnce.
[tex]s_1,\ s_2[/tex] = sample standard deviations .
Given : [tex]{\overline{x}_1=12,\ \ \overline{x}_2=9[/tex]
[tex]s_1=5,\ \ s_2=3[/tex]
[tex]n_1=13,\ n_2=10[/tex]
Then, the standard deviation of the difference between the two means will be :
[tex]SD_{\overline{x}_1-\overline{x}_2}=\sqrt{\dfrac{(5)^2}{13}+\dfrac{(3)^2}{10}}[/tex]
[tex]=\sqrt{\dfrac{25}{13}+\dfrac{9}{10}}\\\\=\sqrt{\dfrac{367}{130}}=1.68020145312\approx1.680[/tex]
The nearest option : B. 1.679
Hence, the standard deviation of the difference between the two means = 1.679
