SOLUTION: 9.51 A can of peeled whole tomatoes is supposed to contain an average of 19 ounces of tomatoes (excluding the juice). The actual weight is a normally distributed random variable w

Question 207986This question is from textbook Applied Statistics in Business and Economics (Doane and Seward)
: 9.51 A can of peeled whole tomatoes is supposed to contain an average of 19 ounces of tomatoes
(excluding the juice). The actual weight is a normally distributed random variable whose standard
deviation is known to be 0.25 ounces. (a) In quality control, would a one-tailed or two-tailed test
be used? Why? (b) Explain the consequences of departure from the mean in either direction.
(c) Which sampling distribution would you use if samples of four cans are weighed? Why? (d) Set
up a two-tailed decision rule for α = .01.
This question is from textbook Applied Statistics in Business and Economics (Doane and Seward)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
9.51 A can of peeled whole tomatoes is supposed to contain an average of 19 ounces of tomatoes (excluding the juice).
The actual weight is a normally distributed random variable whose standard
deviation is known to be 0.25 ounces.
(a) In quality control, would a one-tailed or two-tailed test
be used? Why?
One-tail. We're only interested whether the cans are underweight.
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(b) Explain the consequences of departure from the mean in either direction.
If below they are not meeting the standard.
If above it's the companies loss. Tough.
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(c) Which sampling distribution would you use if samples of four cans are weighed? Why?
The T-distribution since n is so small.
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(d) Set up a two-tailed decision rule for α = .01.
Using IvT(0.005,3) = -5.8409..
Rule: Reject Ho if the test statistic is less than -5.8509..
or greater than 5.8409..
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Cheers,
Stan H.
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