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 96.6% of the people who have that disease. However, it erroneously gives a positive reaction in 4.8% 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." a) What is the probability of Type I error? (Round your answer to 2 decimal places.) b. What is the probability of Type II error? (Round your answer to 2 decimal places.)

Explanation / Answer

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 96.6% of the people who have that disease. However, it erroneously gives a positive reaction in 4.8% 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."

a) What is the probability of Type I error? (Round your answer to 2 decimal places.)

Note that

Ho: The person does not have the disease.

Ha: The person does have the disease.

As a type I error is incorrectly rejecting Ho, then it is a false positive.

Hence, as given,

P(false positive) = 0.048 [ANSWER]

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b. What is the probability of Type II error? (Round your answer to 2 decimal places.)

Note that

Ho: The person does not have the disease.

Ha: The person does have the disease.

As a type II error is incorrectly failing to reject Ho, then it is a false negative.

Hence,

P(false negative) = 1 - P(true positive) = 1 - 0.966 = 0.034 [ANSWER]

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