The screening process for detecting a rare disease is not perfect. Researchers h
ID: 3220991 • Letter: T
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.
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.
Explanation / Answer
Null Hypothesis Ho: The Individual does not have the disease
Type I error : Null hypothesis is True, but the test rejects Null hypothesis(Ho) . i.e
In our case Type I Error : If The Individual does not have the disease but the test says' The Individual has the disease ' . The test says The Individual has the disease but the truth is the individual does not have disease.
Blood test erroneously gives a positive reaction in 3.3% of the people who do not have the disease;
Probability that the test says the individual has the disease but actual truth is The Individual does not have the disease =3.3/100 = 0.033
Probability of Type I error = 0.033
Type II error: Null Hypothesis is False, But the test Accepts Null hypothesis
In our case,
The individual has the disease but the test says the individaul does not have the disease.
The test says the individaul does not have the disease but the truth is The individual has the disease
Blood test gives a positive reaction in 94.8% of the people who have that disease. i.e
Probability of blood test positive when people have that disease = 94.8/100 = 0.948
Probability of test says that individual has disese when the individual has that disease = 0.948
Probability of test says that individual does not have disease when the individual has that disease = 1 - Probability of test says that individual has disese when the individual has that disease = 1- 0.948 = 0.052
Probability that the test says the individaul does not have the disease but the truth is The individual has the disease 0.052
Proabability of type II error = 0.052