Answer:
c. [1.771;4.245] feet
Explanation:
Hello!
The variable of interest is
X: height of a student at UH
X~N(μ;σ²)
You have to estimate the population standard deviation using a 95% confidence interval.
The statistic to use for the interval is a student Chi-Square with n-1 degrees of freedom. First you have to calculate the CI for the population variance:
![[((n-1)S^2)/(X^2_(n-1;1-\alpha /2)) ;((n-1)S^2)/(X^2_(n-1;\alpha /2)) ]](https://img.qammunity.org/2021/formulas/mathematics/college/zsd33t8kpy3cxq0yo95eu8lrmaaoktn9ct.png)


n=12
S= 2.5
![[(11*6.25)/(21.920) ;(11*6.25)/(3.816)} ]](https://img.qammunity.org/2021/formulas/mathematics/college/t0z49nrklu029jobx7zxkhqyoq9ubosuk9.png)
[3.136; 18.016] feet²
Then you calculate the square root of both limits to get the CI for the population standard deviation:
[√3.136; √18.016]
[1.771;4.245] feet
I hope this helps!