Answer:
c. [1.771;4.245] feet
Step-by-step 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:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{11;0.975}= 21.920[/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{11;0.025}= 3.816[/tex]
n=12
S= 2.5
[tex][\frac{11*6.25}{21.920} ;\frac{11*6.25}{3.816}} ][/tex]
[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!
