Let
n = number of data
s = standard deviation (sample)
S = standard deviation (population)
The working equations is
[tex] \frac{(n-1) s^{2} }{ x^{2}_{right} } \ \textless \ S^{2} \ \textless \ \frac{(n-1) s^{2} }{ x^{2}_{left} }[/tex]
To find [tex]x^{2}_{right}[/tex], : (1 - 0.90)/2 = 0.05
To find [tex]x^{2}_{left}[/tex], : 1 - 0.05 = 0.95
Degrees of freedom = n-1 = 24 - 1 = 23
This is shown in the figure attached. Since there is no row for df=23, we interpolate. Thus,
[tex]x^{2}_{left} = 13.093[/tex]
[tex]x^{2}_{right} = 35.17[/tex]
Substitute all values,
[tex] \frac{(24-1) 5.6^{2} }{ 35.17} \ \textless \ S^{2} \ \textless \ \frac{(24-1)
5.6^{2} }{ 13.093} }[/tex]
Thus the answer is,
[tex]20.51\ \textless \ S^{2} \ \textless \ 55.09[/tex]