SOLUTION: The GMS Company packages their wood mulch in 50-kilogram bags. The packaging department reports that the standard deviation of this process is 1.36 kilograms per bag. At the en

Question 1192021: The GMS Company packages their wood mulch in 50-kilogram bags. The
packaging department reports that the standard deviation of this process is 1.36
kilograms per bag. At the end of each day, the production manager, weighs 160
bags and computes the mean weight of the sample of 49.2 kilograms. Can it be
concluded that the mean weight of the sample is less than 50 kilograms? Use the
0.01 significant level.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
standard deviation = 1.36
sample size = 160
sample mean = 49.2
critical z-score at one tail .01 significance level = -2.33.
critical z-score at two tail .01 significance level = -2.58
standard error = 1.36 / sqrt(160) = .1075
z-score = (49.2 - 50) / .1075 = -7.44.
this is way greater than the critical z-score.
the results are significant.
you can conclude that the mean weight of the sample is definitely less than 50 kilograms.

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