A company that produces snack foods uses a machine to packag

A company that produces snack foods uses a machine to package 454 oz bags of peanuts. We will assume that the net weights are normally distributed with mean 454 oz and that the standard deviation of all such weights are as follows: Use the p-value method. Show work.

A) Null hypothesis: ?
B) Alternative hypothesis: ?
C) test statistic: ?
D) p-value: ?
E) initial conclusion: ?
F) conlsuion: ?

Solution

A Null Hypothesis
Ho : mu= 454
B Alternative Hypothesis
Ha : mu is not = 454

C Test statistic:
Here we can use the one-sample Z-statistic because the population standard deviation is given.

Z=X-mu/sigma/sqrt(n)=450-454/7.8/sqrt(25)=-2.56

D Computing the P-value
P-Value = 2*P[Z > |-2.56|] = 2*(.0052) = 0.0105 or 1.05%

E Reject Ho with a = 0.10 if: zobs >zalpha/2= 1.645 OR zobs-zalpha /2= - 1.645

F Since -2.56 falls inside the rejection region, the test rejects the null hypothesis. Our conclusion
should be that the true mean weight of a bag of peanuts packaged by the machine is not equal to
454 oz. Therefore the packaging machine is not working properly.