a. The event that the test is positive is dependent on the event that the person has the disease.
b. The event that the test is positive is dependent on the event that the person has the disease.
Part A: The probability that a person has the disease, given that the test is positive, is the positive predictive value (PPV).
PPV = (number of true positives) / (total number of positive results
PPV = 65 / (65 + 16) = 0.8023
Therefore, the probability that a person has the disease, given that the test is positive, is 80.23%.
Part B: The event that the test is positive, given that the person has the disease, is dependent on the event that the person has the disease
This is because knowing that a person has the disease increases the probability that the test will be positive. For example, the table shows that 65 out of 90 people with renal disease tested positive for the disease. This means that 65/90 = 0.7222, or 72.22%, of people with renal disease will test positive for the disease.
If we did not know whether or not the person had the disease, the probability that the test would be positive would be different. For example, the table shows that 81 out of 150 people tested positive for the disease. This means that 81/150 = 0.54, or 54%, of people will test positive for the disease, regardless of whether or not they have the disease.
Therefore, the event that the test is positive is dependent on the event that the person has the disease.
Complete question:
A researcher carried out a diagnostic study on 150 people, 90 of whom had been diagnosed with renal disease and 60 who were known to be healthy, to evaluate how well a diagnostic test works to detect renal disease. the results of the experiment are shown in the table below Part A: If a person has the disease, what is the probability that the test is positive? Part B: Is the event that the test is positive, given that the person has the disease, dependent or independent?