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5.6.11. The rates of return (rounded to the nearest percentage) for 25 clients of a financial firm are given in the following table. 13 11 28 6 -4 15 13 6 11 11 3 12 20 3 16 16 15 8 20 15 4 1 12 2 -9 Find a 98% confidence interval for the variance σ2 of rates of return. Use this to find the confidence interval for the population standard deviation, σ.

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(x-X) 3.080 1.080 18.080 3.920 13.920 5.080 3.080 3.920 1.080 1.080 -6.920 2.080 10.080 -6.920 6.080 6.080 5.080 1.920 10.080 5.080 -5.920 -8.920 2.080 -7.920 18.920 (x-X) 9.4864 1.1664 326.8864 15.3664 193.7664 25.8064 9.4864 15.3664 1.1664 1.1664 47.8864 4.3264 101.6064 47.8864 36.9664 36.9664 25.8064 3.6864 101.6064 25.8064 35.0464 79.5664 4.3264 62.7264 357.9664 S.No 13.000 11.000 28.000 6.000 -4.000 15.000 13.000 6.000 11.000 11.000 3.000 12.000 20.000 3.000 16.000 16.000 15.000 8.000 20.000 15.000 4.000 1.000 12.000 2.000 9.000 248 9.920 2 4 10 12 15 16 19 25 1571.8400 s-E(x-x)2/(n-1)- 65.493 here n 25 65.49 Critical value for 24 degree of freedom and 98 % CI are as follows 10.856 0.01 42.980 0.99 (n-1)s/x Variance Cl- Variance CI 36.571 144.790 Std deviation CI 6.047 12.033

from above 98% confidence interval for population variance =36.571 to 144.790

98% confidence interval for population standard deviation =6.047 to 12.033

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