Mike is 15 years old and Rose is 13 years old. One day they went to see the doctor. Because they had bad colds and coughed terribly. After checking, the doctor gave them two bottles of medicine to take. There are the words on the mark of the bottles:

椭圆$\frac{x^2}{34}+\frac{y^2}{n^2}=1$和双曲线$\frac{x^2}{n^2}-\frac{y^2}{16}=1$有相同的焦点，则实数$n$的值是 （    ）