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 97.1% of the people who have that disease. However, it erroneously gives a positive reaction in 4.7% 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.)
Added by Ashley H.
Step 1
A Type I error occurs when we reject the null hypothesis when it is actually true. In this case, the null hypothesis is "the individual does not have the disease". So, a Type I error would occur if the test gives a positive result (indicating the person has the Show more…
Show all steps
Close
Your feedback will help us improve your experience
Jyoti Rajak and 56 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Audrey F.
The probability that a person has a certain disease is 0.05. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.90. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.03. a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present? b. If the medical diagnostic test has given a negative result (indicating that the disease is not present), what is the probability that the disease is not present? a. The probability is ............(Round to three decimal places as needed.) b. The probability is ...... .......(Round to three decimal places as needed.)
Sri K.
Suppose that we have a test for a rare disease, and the test is 97 percent accurate. Given a population of 10000 people, of whom 2 percent have the disease, answer the following questions. You may give exact answers, or decimals rounded to three decimal places. How many people have the disease? How many people who have the disease test positive for the disease? How many people do not have the disease? How many people who do not have the disease test positive for the disease? If someone tests positive for the disease, what is the probability that they actually have the disease? If someone tests negative for the disease, what is the probability that they actually do not have the disease?
Aarti K.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD