The screening process for detecting a rare disease is not pe

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 94.4% of the people who have that disease. However, it erroneously gives a positive reaction in 3.9% 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.

Solution

a.

Type I error is the probability of rejecting the null hypothesis when it is true. Here the null hypothesis \"the individual does not have the disease\". That is type I error is the probability of concluding that person has disease while person actually does not have disease. Since test  gives a positive reaction in 3.9% of the people who do not have the disease so the probability of Type I error is 3.9% or 0.039.

b.

Type II error is the probability of not rejecting the null hypothesis when it is false. Here the null hypothesis \"the individual does not have the disease\". That is type II error is the probability of concluding that person does not has disease while person actually have disease. Since test  gives a positive reaction in 94.4% of the people who have the disease so it gives negative reaction 1-94.4% = 5.6% of the people who have the disease so the probability of Type II error is 5.6% or 0.056.