A container of car oil is supposed to contain 1000 millilite

A container of car oil is supposed to contain 1000 milliliters of oil. A quality control manager wants to be sure that the standard deviation of the oil containers is less than 20 milliliters. He randomly selects 10 cans of oil with a mean of 997 milliliters and a standard deviation of 32 milliliters. Use these sample results to construct a 95% confidence interval for the true value of sigma. Does this confidence interval suggest that the variation in the oil containers is at an acceptable level?

Solution

3.

As              
              
df = n - 1 =    9          
alpha = (1 - confidence level)/2 =    0.025          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    19.0227678          
chi^2(alpha/2) =    2.7003895          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    484.4720862          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    3412.840999          
              
Thus, the confidence interval for the variance is              
              
(   484.4720862   ,   3412.840999   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   22.01072662   ,   58.41952584   )

As this whole interval is greater than 20, then this confidence interval suggests that the variation in the oil containers IS NOT at an acceptable level. [CONCLUSION]

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