Two local farmers, John and Brian, supply pumpkins to a local grocery store. Wei
ID: 2936241 • Letter: T
Question
Two local farmers, John and Brian, supply pumpkins to a local grocery store.
Weights of pumpkins from John’s farm are normally distributed with mean 15 pounds and standard deviation 3 pounds.
Weights of pumpkins from Brian’s farm are normally distributed with mean 25 pounds and standard deviation 2 pounds.
John and Brian do not use any packaging on their pumpkins, so the store manager often has to determine the actual supplier, that is, to test the competing hypotheses:
H0: The pumpkin is from John’s farm versus Ha: The pumpkin is from Brian’s farm.
The manager plans to use the following rule:
If a pumpkin weighs 19 pounds or more, the manager will decide that it is from Brian’s farm (Ha),
but if it weighs less than 19 pounds, the manager will decide it is from John’s farm (H0).
For this situation, determine the level of significance for this test?
0.0228
0.0013
0.0968
0.003
0.0918
0.9772
0.9987
0.9032
0.9970
0.9082
Find the power of this test?
0.0228
0.0013
0.0968
0.003
0.0918
0.9772
0.9987
0.9032
0.9970
0.9082
For this situation, find the value of ?
0.0228
0.0013
0.0968
0.003
0.0918
0.9772
0.9987
0.9032
0.9970
0.9082
Explanation / Answer
1)level of signficance =P(John farm pumpkin wight is more then 19) =P(Z>(19-15)/3)=P(Z>1.333)=0.0918
therefore option 0.0918 is correct
2)
power of this test =P( rejecting null when it is correct)=P( Brian pumpkin wight is more then 19) =P(X>19)
=P(Z>(19-25)/2) =P(Z>-3) =0.9987
3)
value of =1-power =0.0013
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