The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97.0% of the people who have that disease. However, it erroneously gives a positive reaction in 3.5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions.
Added by John H.
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This can be calculated using the formula for conditional probability: P(positive reaction | not having the disease) = 3.5%. Show more…
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The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97.1% of the people who have that disease. However, it erroneously gives a positive reaction in 4.7% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions. a. What is the probability of a Type I error? (Round your answer to 3 decimal places.) b. What is the probability of a Type II error? (Round your answer to 3 decimal places.)
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The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.6% of the people who have that disease. However, it erroneously gives a positive reaction in 4.1% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions. a. What is the probability of a Type I error? (Round your answer to 3 decimal places.) b. What is the probability of a Type II error? (Round your answer to 3 decimal places.)
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A rare disease exists with which only 1 in 500 individuals is affected. A test for the disease exists, but of course, it is not infallible. A true-positive result (patient actually has the disease) occurs 95% of the time, while a false-positive result (patient does not have the disease) occurs 1% of the time. If a randomly selected individual is tested and the result is positive, what is the probability that the individual doesn't have the disease?
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