SOLUTION: Can you please help me with this problem? The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 wit

Question 256273: Can you please help me with this problem?
The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 with a standard deviation of 0.41 ounces.

a) What is the appropriate null and alternate hypothesis to determine if the packages
are under filled?

b) What is the p-value for the hypothesis test?

c) Using α = 0.01, draw a conclusion for the hypothesis test. Make sure you state
your conclusion in the context of the problem.

d) Using α = 0.05, draw a conclusion for the hypothesis test. Make sure you state
your conclusion in the context of the problem.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 with a standard deviation of 0.41 ounces.
a) What is the appropriate null and alternate hypothesis to determine if the packages are under filled?
Ho: u >= 18
H1: u < 18
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b) What is the p-value for the hypothesis test?
The test statistic is t = (17.78-18)/[0.41/sqrt(18)] = -0.22/0.09664
= -2.2765
---
So the p-value is
P(t<-2.2765 when df = 17) = tcdf(-100,-2.2765,17) = 0.01802..
--------------------------
c) Using α = 0.01, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.
---
Since the p-value is greater than 1%, we fail to reject Ho.
Based on this test we do not believe the rolled oats packages are under filled.
------------------------
d) Using α = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.
---
Since the p-value is less than 5% we reject Ho.
Based on this test we conclude the rolled oats packs do not contain at least
18 ounces.
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Cheers,
Stan H.

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