The manufacturer of bags of cement claims that they fill each bag with 50 pounds
ID: 3388609 • Letter: T
Question
The manufacturer of bags of cement claims that they fill each bag with 50 pounds of cement. Assume that the amount filled in each bag follows a normal distribution with standard deviation 1.2 pounds. However, there was some complaint that the bags are under-filled with mean filling amount 49 pounds of cement each bag. The decision rule is adopted to shut down the filling machine if the sample mean weight for a sample of 20 bags is below 49.5 lb.
1. If you are asked to construct a test of 2% level of significance, what will be your decision rule (i.e., write the rejection region for = 0.02)? State clearly what is your test-statistic.
Explanation / Answer
Test Statistic
Population Mean(U)=49
Given That X(Mean)=49.5
Standard Deviation(S.D)=1.2
Number (n)=20
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=49.5-49/(1.2/Sqrt(20)
Zo =1.8634
The Value of |Z | at LOS 0.05% is 2.054
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