Answer)
Given confidence level is 90%.
Variance = 65.6*65.6 = 4303.36
N = 25
Formula for confidence interval is
√{(n-1)*s^2}/√x^2(alpha/2) < sigma < √{(n-1)*s^2}/√x^2(1 - (alpha/2)}
Alpha = 1 - confidence level
S^2 sample.variance
N-1 = degrees of freedom
Degrees of freedom = n-1 = 24
Alpha = 1 - 0.9 = 0.1
For low end alpha/2 = 0.05
From chi square table, for 0.05 alpha and 24 df
X^2 = 36.415
So low end. = 53.2561
Upper end
Alpha = 1 - (alpha/2) = 0.95
For 0.95 alpha and 24 df
X^2 = 13.8484
Upper end = 86.3594
Required interval is
53.2561 < sigma < 86.3594
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