Find the 95% confidence interval for the variance of the heights of maple trees if a sample of 11 trees has a standard deviation of 10.2 feet.
A) $93.0

Question

Find the 95% confidence interval for the variance of the heights of maple trees if a sample of 11 trees has a standard deviation of 10.2 feet. 
A) $93.0 < \sigma ^ { 2 } < 115.0$
B) $7.1 < \sigma ^ { 2 } < 17.9$
C) $9.2 < \sigma ^ { 2 } < 11.2$
D) $50.8 < \sigma ^ { 2 } < 320.4$

Quizplus · Accepted Answer

The confidence interval for the variance is calculated using the chi-square distribution. With a sample size of 11, the degrees of freedom is 10. Using the sample standard deviation of 10.2 feet, the interval is calculated as $ \left( \frac{(n-1)s^2}{\chi^2_{0.975}}, \frac{(n-1)s^2}{\chi^2_{0.025}} \right) $, which results in the interval $50.8 < \sigma^2 < 320.4$.

Find the 95% Confidence Interval for the Variance of the Heights