Using the Chi-Square distribution table, the confidence interval for the standard deviation of the height of students at uh is (2.20, 5.26)
The following formulas provide the standard deviation's confidence interval:
[tex](\sqrt{\frac{(n-1)(s)^{2} }{X^{2}_{n-1,\alpha/2 } } } , \sqrt{\frac{(n-1)(s)^{2} }{X^{2}_{n-1, 1-\alpha /2} } }[/tex]
Given parameters:
n= 12 ; s= 3.1
Significance level :
[tex]\alpha - 1 = 1 - 0.95 = 0.05[/tex]
Using Chi-square distribution table,
[tex]X^{2} _{11, 0.025} =21.95\\\\X^{2} _{11, 0.975} = 3.82[/tex]
Currently, the following equations provide the 95% confidence interval for the standard deviation of students' heights at UH:-
[tex](\sqrt{\frac{(11)(3.1)^{2} }{21.92 } } , \sqrt{\frac{(11)(3.1)^{2} }{3.82 } } =(2.20, 5.26)[/tex]
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