SOLUTION: A packaging device is set to fill detergent packets with a mean weight of 150 grams. The standard deviation is known to be 5.0 grams.It is important to check the machine periodical

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Question 1194790: A packaging device is set to fill detergent packets with a mean weight of 150 grams. The standard deviation is known to be 5.0 grams.It is important to check the machine periodically because if it is overfilling it increases the cost of the materials , whereas if it is under filling the firm is liable to prosecution. A random sample of 25 filled boxes is weighed and shows a mean net weight of 152.5 grams. Can we conclude that the machine is no longer producing the 150 grams quantities? Use 5% significant.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Ho: P=150 gm
Ha: P NE 150 gm
alpha=0.05 p{reject Ho|Ho true}
test is a z(x bar-mean)/sigma/sqrt(n)
critical value is |z|>1.96
calculation is z=(152.5-150)/5.0/sqrt(25)
z=2.5(1)=2.5
reject Ho.
There is evidence that there is overfilling at the 5% level. p-value is 0.0062.