Answer:
The answer is "[tex](-33.9218,-16.0782)\\\\[/tex]".
Step-by-step explanation:
Calculating the critical value:
Freedom Degree= 7.
The significance level, [tex]\alpha= 0.05[/tex]
Using excel function the critical value:
[tex]\to t_{\frac{\alpha}{2} (df)}=t_{\frac{0.05}{2},7}\\\\=T.INV.2T(0.05,7)\\\\=\pm 2.3646\\\\[/tex]
When [tex]95\%[/tex] of the confidence intervals for the difference of means:
[tex]\to (\bar{x_1}-\bar{x_2}) \pm t_{\frac{\alpha}{2}}\sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}\\\\=(90-115) \pm 2.3646 \sqrt{\frac{5^2}{8}+\frac{102^2}{9}}\\\\=-25 \pm 2.3646 (3.773077)\\\\=(-33.9218,-16.0782)\\\\[/tex]
