The screening process for detecting a rare disease is not perfect. Researchers h

Question

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 94.5% of the people who have that disease. However, it erroneously gives a positive reaction in 1.5% of the people who do not have the disease. Answer the following questions using the null hypothesis as "the individual does not have the disease." What is the probability of Type I error? (Round your answer to 2 decimal places.) Probability What is the probability of Type II error? (Round your answer to 2 decimal places.) Probability

Explanation / Answer

a)

Note that a type I error is incorrectly rejecting the null hypothesis.

As

Ho: The patient does not have the disease.
Ha: The patient does have the disease.

Hence, it is a false positive,

P(type I) = 0.015 [ANSWER]

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b)

Note that a type II error is incorrectly failing to reject the null hypothesis.

As

Ho: The patient does not have the disease.
Ha: The patient does have the disease.

Hence, it is a false negative,

P(type I) = 1 - 0.945 = 0.055 [ANSWER]

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