The manufacturer of bags of cement claims that they fill eac

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.

Solution

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