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 94.2% of the people who have that disease. However, it erroneously gives a positive reaction in 2.7% 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 a Type I error? (Round your answer to 3 decimal places.)
  

b. What is the probability of a Type II error? (Round your answer to 3 decimal places.)
  

Answer 1

a)
The probability that incorrectly gives a positive reaction in 0.027

probability that of the people who do not have the disease.

This is the type I error.

The required probability is, 2.7% = 0.027 of the people who do not have the disease that means that he reject Ho when the individual not have the disease

b)
The probability that people who have that disease is 0. 942.This is power of the test.

The required probability is, 1 - 0.942 = 0.058

the probability of Type II error is 0.058
.
the probbility that positive reaction with the people that has the disease so the complement is the neg. reaction with the people that has the diseas