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Suppose the frequency of true casual claims in medicine is 1/10-one tenth of the claims to the effect that this pathogen causes this disease, that poison has an effect on development, or this new medicine is effective in relieving those symptoms are true. Suppose we accept a causal claim if and only if we infer that there is a probabilistic dependence between the relevant cause and effect variables, and we test for probabilistic dependence using classical hypothesis testing with a null hypothesis that there is no probabilistic dependence, with a significance level of .05 and a power of .25. Assume we test each causal hypothesis just once. 4. Suppose we test a particular hypothesis 5 times, and see a significant result in 2 of these tests. What is the chance that the casual claim is false, given the data?

Suppose the frequency of true casual claims in medicine is 1/10-one tenth of the claims to the effect that this pathogen causes this disease, that poison has an effect on development, or this new medicine is effective in relieving those symptoms are true. Suppose we accept a causal claim if and only if we infer that there is a probabilistic dependence between the relevant cause and effect variables, and we test for probabilistic dependence using classical hypothesis testing with a null hypothesis that there is no probabilistic dependence, with a significance level of .05 and a power of .25. Assume we test each causal hypothesis just once. 4. Suppose we test a particular hypothesis 5 times, and see a significant result in 2 of these tests. What is the chance that the casual claim is false, given the data?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose the frequency of true casual claims in medicine is 1/10-one tenth of the claims to the effect that this pathogen causes this disease, that poison has an effect on development, or this new medicine is effective in relieving those symptoms are true. Suppose we accept a causal claim if and only if we infer that there is a probabilistic dependence between the relevant cause and effect variables, and we test for probabilistic dependence using classical hypothesis testing with a null hypothesis that there is no probabilistic dependence, with a significance level of .05 and a power of .25. Assume we test each causal hypothesis just once. 4. Suppose we test a particular hypothesis 5 times, and see a significant result in 2 of these tests. What is the chance that the casual claim is false, given the data?
Transcribed Image Text:Suppose the frequency of true casual claims in medicine is 1/10-one tenth of the claims to the effect that this pathogen causes this disease, that poison has an effect on development, or this new medicine is effective in relieving those symptoms are true. Suppose we accept a causal claim if and only if we infer that there is a probabilistic dependence between the relevant cause and effect variables, and we test for probabilistic dependence using classical hypothesis testing with a null hypothesis that there is no probabilistic dependence, with a significance level of .05 and a power of .25. Assume we test each causal hypothesis just once. 4. Suppose we test a particular hypothesis 5 times, and see a significant result in 2 of these tests. What is the chance that the casual claim is false, given the data?
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