Answer to Question #140585 in Statistics and Probability for Beaulah

Question

The table below shows the heights (in meters) of a random sample of seven cedar trees.



Tree

A

B

C

D

E

F

G

Height

15

13

11

9

7

5

10



Use the data provided to estimate the unknown variance of the entire population of cedar trees with a 99 % degree of confidence.

Answer 1

n=7

variance =11.67

$\alpha=0.01$

$CI =\frac{(n-1)s^2}{\chi^2_R}<\sigma^2<\frac{(n-1)s^2}{\chi^2_L}$

$\chi^2_L$ and $\chi^2_R$ are left tailed and right tailed critical values of Chi square respectively.

$\chi^2_L=\chi^2_{0.005,6}=0.6757$

$\chi^2_R=\chi^2_{0.995,6}=18.5476$

$CI =\frac{6\times11.67}{18.5476}<\sigma^2<\frac{6\times11.67}{0.6757}$

$=3.775<\sigma^2<103.626$

={3.77,103.626}