Cans of paint are labeled as containing 1 gallon, so the machine used to fill th

Question

Cans of paint are labeled as containing 1 gallon, so the machine used to fill them is set to dispense slightly more than a gallon, to reduce the likelihood a can contains less than a gallon. To evaluate the performance of the machine, a sample of 12 cans is filled. The mean volume of paint in the 12 cans is 1.011 gallons and the standard deviation of the paint in the 12 cans is 0.014 gallons. 1) Calculate a 95% lower confidence bound for mean can contents, . Based on your answer to part (a), do you believe with 95% confidence that the mean volume of paint that a machine is putting into a can is greater than 1 gallon? Explain your answer using information from part (a) a) b)

Explanation / Answer

a) here std error of mean =std deviation/(n)1/2 =0.014/(12)1/2 =0.0040

for 95% lower bound and (n-1=11) degree of freedom ; critical value of t =-1.7958

hence 95% lower bound for mean =sample mean +z*std error =1.011 -1.7958*0.0040 =1.0037

b) as our lower 95% confidence bound has value greater then 1; therfore we can conclude with 95% confidence that the mean volume of paint that a machine is putting into a can is greater then 1 gallon.

please revert for any clarification

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