4. Based on the "Structure of a Hypothesis Test", fully describe the hypothesis test for the scenario in question 3, assuming a=0.01 and that he finds that only 52 out of 1000 bushels of his crop are lost to insect infestations.

College Algebra (MindTap Course List)
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Author:R. David Gustafson, Jeff Hughes
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Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 5E: List the sample space of each experiment. Rolling one die and tossing one coin
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4. Based on the "Structure of a Hypothesis Test", fully describe the hypothesis test for the
scenario in question 3, assuming a=0.01 and that he finds that only 52 out of 1000 bushels of his
crop are lost to insect infestations.
Transcribed Image Text:4. Based on the "Structure of a Hypothesis Test", fully describe the hypothesis test for the scenario in question 3, assuming a=0.01 and that he finds that only 52 out of 1000 bushels of his crop are lost to insect infestations.
4.
1) Hypotheses:
Нoip-0.07 На:p<0.07
2) Decision Rule: We will reject the null hypothesis when the likelihood of observing
something as small or smaller than X= 52 out of 1000 bushels is no larger than a 1%
probability, under the assumption of the null hypothesis. That is,
(X52|p=0.07)<0.01
3) We will reject HO if the observed value of X=52 is smaller than some cutoff value of
х.
4) Based on the sample evidence, we will either:
a. Reject HO in favor of p<0.07 of insect-related crop destruction for the farmer's new
method.
b. Fail to reject HO. We do not have sufficient evidence to conclude that the farmer's
new method is better than his old method.
Transcribed Image Text:4. 1) Hypotheses: Нoip-0.07 На:p<0.07 2) Decision Rule: We will reject the null hypothesis when the likelihood of observing something as small or smaller than X= 52 out of 1000 bushels is no larger than a 1% probability, under the assumption of the null hypothesis. That is, (X52|p=0.07)<0.01 3) We will reject HO if the observed value of X=52 is smaller than some cutoff value of х. 4) Based on the sample evidence, we will either: a. Reject HO in favor of p<0.07 of insect-related crop destruction for the farmer's new method. b. Fail to reject HO. We do not have sufficient evidence to conclude that the farmer's new method is better than his old method.
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