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 96.5% of the people who have that disease. However, it erroneously gives a positive reaction in 1.0% 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. What is the probability of Type I error? (Round your answer to 3 decimal places.) What is the probability of Type II error? (Round your answer to 3 decimal places.)

Explanation / Answer

Here the null hypothesis is that "The individual does not have the disease "

a) The probability of Type I error would be:

Type I error occurs when the null hypothesis is true but is rejected. That is in this case the individual does not have the disease but the test is positive. This happens when it erroneously gives a positive reaction in 1% of the people who does not have the disease. Therefore the probability of type I error here is 0.01

b) The probability of Type II error here would be:

A type II error happens when a null hypothesis is false but it is accepted. That is in this situation the person does actually have the disease but it is not detected. Therefore the probability of type II error here would be: 1- 0.965 = 0.035

Therefore final answers are:

a) 0.01

b) 0.035

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