Answer: (1.64,4.01)
Step-by-step explanation:
The confidence interval for the population variance is given by :-
[tex]\left ( \dfrac{(n-1)s^2}{\chi^2_{n-1,\alpha/2}},\ \dfrac{(n-1)s^2}{\chi^2_{n-1,1-\alpha/2}} \ \right )[/tex]
Given : n= 69 ; [tex]s^2=2.46[/tex]
Significance level : [tex]\alpha=1-0.99=0.01[/tex]
Using Chi-square distribution table ,
[tex]\chi^2_{68,0.005}}=101.77592\\\\\chi^2_{68,0.995}}=41.71347[/tex] [by using chi-square distribution table]
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
[tex]\left ( \dfrac{(68)(2.46)}{101.77592},\ \dfrac{(68)(2.46)}{41.71347} \ \right )\\\\=\left ( 1.64361078731, 4.01021540524\right )\approx(1.64,\ 4.01)[/tex]
Hence, the 99% confidence interval for the population variance of the weights of all axles in this factory is (1.64,4.01).
