Testing for Alzheimer's disease can be a long and expensive process. Recently, a group of researchers devised a 7min test to serve as a quick screen for the disease. A patient who tested positive would then go through the more expensive battery of tests and medical diagnosis. The authors reported a false positive rate of 4% and a false negative rate of 8%
A) Put this in context of a hypothesis test. What are the null and alternative hypotheses?
B)What would a Type 1 error mean?
C)What would a Type 2 error mean?
D)Which would be worse? Explain
Any help on this would be really appreciated! I missed school all last week and didn't get to learn this so I'm really lost. Thanks! =]
Gucci
A) In the context of a hypothesis test, the null hypothesis (H0) would be that the patient does not have Alzheimer's disease, and the alternative hypothesis (H1) would be that the patient does have Alzheimer's disease.
B) A Type 1 error, also known as a false positive, would occur if the test incorrectly identifies a patient as having Alzheimer's disease when they do not actually have it. In this case, a Type 1 error would mean that the patient is referred for further expensive tests and medical diagnosis, even though they do not have the disease.
C) A Type 2 error, also known as a false negative, would occur if the test incorrectly identifies a patient as not having Alzheimer's disease when they actually do have it. In this case, a Type 2 error would mean that the patient is not referred for further tests and diagnosis, potentially delaying the proper treatment and management of their condition.
D) In this scenario, a Type 2 error would be considered worse. This is because a false negative result would mean that a patient who actually has Alzheimer's disease would be missed, potentially delaying their treatment and management. On the other hand, a false positive (Type 1 error) would lead to further testing and diagnosis, which might be costly and time-consuming, but it would not delay treatment for those who do have the disease.
It's important to note that the relative severity of Type 1 and Type 2 errors can vary depending on the specific context and consequences of the disease being tested.