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 95.0% of the people who have that disease. However, it erroneously gives a positive reaction in 2.5% 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.
(a) What is the probability of Type I error? (Round your answer to 3 decimal places.)
(b) What is the probability of Type II error? (Round your answer to 3 decimal places.)

Answer 1

Answer:

Probability of Type I error: 0.025

Probability of Type II error: 0.050

Step-by-step explanation:

$H_{0}$: "the individual does not have the disease"

(a) Probability of Type I error = Probability of rejecting $H_{0}$ when $H_{0}$ is true = Probability of concluding the individual has the disease when in fact the individual does not have the disease = 0.025 because the blood test erroneously gives a positive reaction in 2.5% of the people who do not have the disease.

(b) Probability of Type II error = Probability of fail to reject $H_{0}$ when $H_{1}$ is true = Probability of concluding the individual does not have the disease when in fact he has the disease = 0.05 because the blood test gives a positive reaction in 95% of the people who have the disease, this implies that the test gives a negative reaction in %5 of the people who have the disease.