Answer: [tex](2.20,\ 5.26)[/tex]
Step-by-step explanation:
The confidence interval for the 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 : n= 12 ; s= 3.1
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Using Chi-square distribution table ,
[tex]\chi^2_{11,0.025}}=21.92\\\\\chi^2_{11,0.975}}=3.82[/tex]
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
[tex]\left ( \sqrt{\dfrac{(11)(3.1)^2}{21.92}},\ \sqrt{\dfrac{(11)(3.1)^2}{3.82}} \ \right )\\\\=\left ( 2.19602743525, 5.26049188471\right )\approx(2.20,\ 5.26)[/tex]
A 95% confidence interval for the standard deviation of the height of students at UH (2.20, 5.26)
The confidence interval is given by:
[tex]\sqrt{(n-1)s^2/X^2n-1, \alpha/2} , \sqrt{(n-1)s^2/X^2n-1, 1-\alpha /2}[/tex]
Given
Significance level : [tex]\alpha[/tex] =1 - 0.95
= 0.05.
Using Chi-square distribution table ,
[tex]X^2 1, 0.025 = 21.92\\X^2 1, 0.975 = 3.82[/tex]
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by:-
(2.20, 5.26)
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