The customary medicine for treating a certain illness gives positive results 50% of the time. A...
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The customary medicine for treating a certain illness gives positive results 50% of the time. A new preparation is proposed, and to test its advantages we plan to use it in ten cases. Here we agree that the advantage for the new preparation will be considered as proved if it gives a positive result in no less than eight cases out of the ten. H₁: p=5 H₁ :p> 5 In this test by rejecting H, in favor of H, we may get a wrong result with probability approximately 0.05. a) Verify this using the binomial distribution. b) We can approximate the binomial distribution with the normal distribution with mean value 5 and standard deviation root(2.5). Verify that by rejecting H, in favor of H, we may get a wrong result with probability approximately 0.05 using the normal distribution. To reduce the probability of this error to about 0.01 without increasing the number of experiments n = 10, we will need to agree that the advantage of the new preparation is proved if it gives a positive result in no less than nine cases out of the ten. c) Verify that, with the new criterion, by rejecting H, in favor of H, we may get a wrong result with probability approximately 0.01. (You may use either binomial distribution or normal distribution.) The customary medicine for treating a certain illness gives positive results 50% of the time. A new preparation is proposed, and to test its advantages we plan to use it in ten cases. Here we agree that the advantage for the new preparation will be considered as proved if it gives a positive result in no less than eight cases out of the ten. H₁: p=5 H₁ :p> 5 In this test by rejecting H, in favor of H, we may get a wrong result with probability approximately 0.05. a) Verify this using the binomial distribution. b) We can approximate the binomial distribution with the normal distribution with mean value 5 and standard deviation root(2.5). Verify that by rejecting H, in favor of H, we may get a wrong result with probability approximately 0.05 using the normal distribution. To reduce the probability of this error to about 0.01 without increasing the number of experiments n = 10, we will need to agree that the advantage of the new preparation is proved if it gives a positive result in no less than nine cases out of the ten. c) Verify that, with the new criterion, by rejecting H, in favor of H, we may get a wrong result with probability approximately 0.01. (You may use either binomial distribution or normal distribution.)
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With the new criterion by rejecting HO in favor of H1 we may get a wrong result with probability app... View the full answer
Related Book For
Federal Taxation 2016 Comprehensive
ISBN: 9780134104379
29th edition
Authors: Thomas R. Pope, Timothy J. Rupert, Kenneth E. Anderson
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