Question

n = 5, s = 4.1, and c = 0.98 Calculate the confidence interval for the population standard deviation from the given values. Round your answers to 1 decimal place. Answer: 1Lower Bound 2Upper Bound

Answer 1

n = 5          

s^2 = 4.1^2 = 16.8100          

% = 98          

Left χ2 value = 0.2971          

Right χ2 value = 13.2767          

Lower limit of the confidence interval (for variance) = (n - 1) * s^2 /Right χ2 value = (5 -1) * 16.81^2/13.276704136185 = 5.0645

Upper limit of the confidence interval (for variance) = (n - 1) * s^2 /Left χ2 value = (5 -1) * 16.81^2/0.297109480573662 = 226.3139

The confidence interval for variance is ( 5.0645 , 226.3139 )      

Lower limit of the confidence interval (for standard deviation) = 2.2504      

Upper limit of the confidence interval (for standard deviation) = 15.0437

The confidence interval for standard deviation is [2.3, 15.0]

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