the confidence interval for the population variance is

(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.
The formula for finding the confidence interval for population variance is:
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.
Here it is given that,
α/2 = 0.02/2 = 0.01
1 - α/2 = 1 - 0.01 = 0.99
For (n - 1) degrees of freedom,
[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)
Using the formula we get,
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]
[tex]730.72 < \sigma^{2} < 4569.53[/tex]
The confidence interval for the population variance is (730.72, 4569.53)
Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.
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