Answer:
The 90% confidence interval for the difference between means is (-161.18, 205.18).
Explanation:
Sample mean and standard deviation for Region I:

![s=\sqrt{(1)/((n-1))\sum_(i=1)^(12)(x_i-M)^2}\\\\\\s=\sqrt{(1)/(11)\cdot [(438-(702))^2+(1013-(702))^2+...+(500-(702))^2+(340-(702))^2]}\\\\\\](https://img.qammunity.org/2021/formulas/mathematics/college/mr5hckrjxu9ipmqe4th3g1cggj1ovdxg00.png)
![s=\sqrt{(1)/(11)\cdot [(69696)+(96721)+...+(131044)]}\\\\\\s=\sqrt{(1174834)/(11)}=√(106803.1)\\\\\\s=326.8](https://img.qammunity.org/2021/formulas/mathematics/college/r2o0utdpp4m7bedv46vofpcqoei6cd6m0x.png)
Sample mean and standard deviation for Region II:

![s=\sqrt{(1)/((n-1))\sum_(i=1)^(15)(x_i-M)^2}\\\\\\s=\sqrt{(1)/(14)\cdot [(778-(680))^2+(464-(680))^2+...+(389-(680))^2+(826-(680))^2]}\\\\\\](https://img.qammunity.org/2021/formulas/mathematics/college/5j1sigxd2jjl39l7nvalzr6jvuf6mbece6.png)
![s=\sqrt{(1)/(14)\cdot [(9551.804)+(46771.271)+...+(84836.27)+(21238.2)]}\\\\\\ s=\sqrt{(545975.7)/(14)}=√(38998)\\\\\\s=197.5](https://img.qammunity.org/2021/formulas/mathematics/college/uzdqs37a4krkcrciuohb9e15ylk1qh6v56.png)
Now, we have to calculate a 90% confidence level for the difference of means.
The degrees of freedom are:

The critical value for 25 degrees of freedom and a confidence level of 90% is t=1.708
The difference between sample means is Md=22.
The estimated standard error of the difference between means is computed using the formula:
The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 90% confidence interval for the difference between means is (-161.18, 205.18).