Answer: (2.2, 5.8)
Step-by-step explanation:
The confidence interval for standard deviation is given by :-
[tex]\left ( \sqrt{\dfrac{(n-1)s^2}{\chi^2_{(n-1),\alpha/2}}} , \sqrt{\dfrac{(n-1)s^2}{\chi^2_{(n-1),1-\alpha/2}}}\right )[/tex]
Given : Sample size : 16
Mean height : [tex]\mu=67.5[/tex] inches
Standard deviation : [tex]s=3.2[/tex] inches
Significance level : [tex]1-0.99=0.01[/tex]
Using Chi-square distribution table ,
[tex]\chi^2_{(15,0.005)}=32.80[/tex]
[tex]\chi^2_{(15,0.995)}=4.60[/tex]
Then , the 99% confidence interval for the population standard deviation is given by :-
[tex]\left ( \sqrt{\dfrac{(15)(3.2)^2}{32.80}} , \sqrt{\dfrac{(15)(3.2)^2}{4.6}}\right )\\\\=\left ( 2.1640071232,5.77852094812\right )\approx\left ( 2.2,5.8 \right )[/tex]
