Reference no: EM131015196
One goal of diagnostic medicine is to develop non-invasive tests to replace, or at least precede, invasive tests. For example, one might want to develop a blood test for liver disease, which alternatively can be tested with a liver biopsy. Two critical measures of goodness for a diagnostic test are the sen sitivity of the test, that is, the proportion of truly positive subjects that test positive; and the specificity of the test, the proportion of truly negative subjects that test negative.
Suppose researchers have just discovered a new version of a diagnostic blood test. Data from 100 subjects were collected. Sixty of the subjects were known healthy patients and 40 had liver disease. The test results are given below.
|
|
Test Result Pos Neg
|
|
|
Known Result
|
Pos
|
38
|
2
|
40
|
|
|
Neg
|
8
|
52
|
60
|
|
46
|
54
|
100
|
(a) Estimate the sensitivity and specificity of the test using 95% confidence intervals.
(b) How large a sample of healthy subjects is needed to estimate specificity within 0.05 units with confidence of 95%?
(c) What is the power of this test to detect an increase of 0.03?
(d) A previous version of this diagnostic test had sensitivity 0.90. Using a = 0.05, test to see if the sensitivity of the new improved test is greater.
|
Difference between pension and postretirement benefits
: What type of pension and other postretirement benefit plans the company offers to its employees? What are the reporting requirements for pension plans in the financial statements?
|
|
Estimate the mean weight of capsules
: Suppose that one is interested in constructing a 95% confidence interval that would estimate the mean weight of capsules to within 2 mg, and you suspect that a is no larger than 3 mg. How large a sample size is necessary?
|
|
Confidence interval for the unknown mean of the population
: Construct a 95% confidence interval for the unknown mean of the pop ulation from which the above sample was obtained. Construct an interval that with 95% confidence will contain 99% of the population values.
|
|
Estimate the non-conforming rate
: If the non-conforming rate has increased to say 12% what is the prob ability that you would see no non-conforming items in a sample of size 8? How large of a sample would you need to estimate the non-conforming rate to within 5% with 95% confide..
|
|
New version of a diagnostic blood test
: Suppose researchers have just discovered a new version of a diagnostic blood test. Data from 100 subjects were collected. Sixty of the subjects were known healthy patients and 40 had liver disease. The test results are given below.
|
|
At what rate is x changing
: A point moves along the curve y = 2x2 - 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x = -3/2?
|
|
Does business interaction in global market conflict
: Review the IMA Statement of Ethical Professional Practice. Does business interaction in the global market conflict with these ethical standards? Consider outsourcing, sustainability, and social responsibility. Is it possible to remain competitive ..
|
|
Confidence interval for the proportion of registered users
: Find a 99% confidence interval for the proportion of registered users with false phone numbers and explain what it indicates. Use language that a manager could easily understand.
|
|
Find the volume of the solid whose base is the given region
: Find the volume of the solid whose base is this region and whose cross-sections perpendicular to the x-axis are the following: squares. semi-circles
|