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 94.8% of the people who have that disease. However, it erroneously gives a positive reaction in 3.3% 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?
b. What is the probability of Type II error?

Answer 1

Probability of Type 1 error = 0.033

Probability of type II error = 0.952

Explanation:

H0: Individual does not have disease

H1: individual has disease

Type 1 error occurs when we fail to accept a correct null hypothesis and accept an alternate Instead

Type ii error occurs when we accept a false null hypothesis instead of the alternate hypothesis

Probability of people with disease = 98.4%

Probability of people without disease = 3.3%

1.probability of type 1 error = 3.3/100

= 0.033

2. Probability of type ii error = (1-98.4%) = 1-0.948

= 0.052