2 A manufacturer is concerned that the 16ounce can of produc

2. A manufacturer is concerned that the 16-ounce can of product \'\'X\'\' is being overfilled. Assume the standard deviation of the process is .03 ounce. The quality-control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounce. At the 5% level of significance, can we conclude that the mean weight is greater than 16 ounce?

Solution

Set Up Hypothesis
Null, mean weight is equal to 16 H0: U=16
Alternate, mean weight is greater than 16 H1: U>16
Test Statistic
Population Mean(U)=16
Given That X(Mean)=16.05
Standard Deviation(S.D)=0.03
Number (n)=50
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=16.05-16/(0.03/Sqrt(50)
Zo =11.7851
| Zo | =11.7851
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =11.7851 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 11.7851 ) = 0
Hence Value of P0.05 > 0, Here we Reject Ho

We have evidence to support mean weight is greater than 16