You work for a soft-drink company in the quality control division. You are inter

Question

You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 17 e oulation stanard devation at a 90% level of confidence 11.9111.9312.16 12.0212.031.79 11.99 12.02 11.93 12.0 12.03 12.07 11.92 1.8112.02 12 11.83 Data checksum: 203.47) Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer a) Find the sample standard deviation: 2 critical values at 90% b) Find the lower and upper confidence: Lower:Upper: c) Report your confidence interval for a:0

Explanation / Answer

Solution:- Given that samples 11.91,11.93,12.16,12.02,12.03,11.79,11.99,12.02,11.93,12.01,12.03,12.07,11.92,11.81,12.02,12,11.83

a) Sample standard deviation = 0.097 = 0.10 (rounded)

b) 90% confidence , n = 17, df = 16

Lower = 7.962 upper = 26.3
c) 90% confidence interval for the standard deviation:-
sqrt((n-1*s^2)/X^2R) < ? < sqrt((n-1*s^2)/X^2L)

= sqrt((16*(0.1^2)/26.3) < ? < sqrt((16*(0.1^2)/7.962)

= 0.07799 < ? < 0.14176

= 0.08 < ? < 0.14

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