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. Write the null and alternative hypotheses.

Solution

Set Up Hypothesis
Null, complaint that the bags are under-filled with mean filling amount 49 pounds H0: U<49
Alternate Hypothesis H1: U>49
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
| Zo | =1.8634
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.8634 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 1.8634 ) = 0.0312
Hence Value of P0.05 > 0.0312, Here we Reject Ho

we don\'t have evidence to that the bags are under-filled with mean filling amount 49 pounds