A container of car oil is supposed to contain 1000 milliliters of oil. A quality
ID: 3393557 • Letter: A
Question
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?Explanation / Answer
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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