Pumpkins 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).
(a) 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
(b) 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
(c) For this situation, find the value of β.
0.0228, 0.0013, 0.0968, 0.003, 0.0918, 0.9772, 0.9987, 0.9032, 0.9970, 0.9082