The meat department of a local supermarket chain packages ground beef using meat

Question

The meat department of a local supermarket chain packages ground beef using meat trays of two sizes: one designed to hold approximately 1 pound of meat, and one that holds approxi- mately 3 pounds. A random sample of 35 packages in the smaller meat trays produced weight measurements with an average of 1.01 pounds and a standard deviation of 0.18 pound. (a) Construct a 99% confidence interval for the average weight of all packages sold in the smaller meat trays by this supermarket chain (b) Suppose that the quality control department of this supermarket chain intends that the amount of ground beef in the smaller trays should be 1 pound on average. Should the confidence interval in (a) concern the quality control department? Explain.

Explanation / Answer

a) std error of mean =std deviation/(n)1/2 =0.0304

for 90% CI and 34 degree of freedom ; t=2.7284

hence 90% confidence interval =sample mean -/+ t*Std error =0.9270 ; 1.0930

b)as above interval contains value below 1 pound till 0.927 pounds which reflects that there is good amount of chance that tray will not be able to hold rated 1 pound which should be a concern to quality team,

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