please show all process including assumptions Testing for Alzheimer\'s disease c
ID: 3041427 • Letter: P
Question
please show all process including assumptions
Testing for Alzheimer's disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. Recently, a group of researchers devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior citizens. A patient who tested positive would then go through the more expensive battery of tests and medical diagnosis. Researchers report that the 7-minute test correctly identifies the disease in 92% of patients who have Alzheimer's disease, and that it is 96% accurate in patients without Alzheimer's disease. Suppose a physician is using the results of the 7-minute test to decide between the following hypotheses: Ho: The patient does not have Alzheimer's disease Ha: The patient does have Alzheimer's disease a. (2 points) using this information, describe what a Type l Error and a Type Il Error would mean in terms of this scenario. b. (2 point) Based on the information above, what would be the values for a and B?Explanation / Answer
(a)
Type I error is the probability of rejecting the true null hypothesis.
In this case type I error is "Reasecher incorrectly conclude that patient does have Alzheimer's disease while actually he does not have Alzheimer's disease".
Type II error is the probability of fail to reject the false null hypothesis.
In this case type II error is
"Reasecher incorrectly conclude that patient does not have Alzheimer's disease while actually he does have Alzheimer's disease".
(b)
P(test positve |disease) = 0.92
P(test negative | does not have disease) = 0.96
Type I error = P(test positive | does not have disease) = 1 - P(test negative | does not have disease) =1 - 0.96 =0.04
Type II error = P(test negative |disease) = 1 -P(test positve |disease)=1 - 0.92 =0.08
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.