The prostate-specific antigen (PSA) test is a simple blood test to screen for prostate cancer. It has been used in men over 50 a
s a routine part of a physical exam, with levels above 4 ng/mL indicating possible prostate cancer. The test result is not always correct, sometimes indicating prostate cancer when it is not present and often missing prostate cancer that is present. Suppose that these are the approximate conditional probabilities of a positive (above 4 ng/ml) and negative test result given cancer is present or absent. In a large study of prostate cancer screening, it was found that about 6.2% of the population has prostate cancer. Draw a tree diagram for selecting a person from this population (outcomes: cancer present or absent) and testing his blood (outcomes: test positive or negative).
1 answer:
The missing table for the Test Result can be expressed as:
Test Result
Positive Negative
Cancer Present 0.21 0.79
Cancer Absent 0.06 0.94
Answer:
Step-by-step explanation:
A tree diagram is an elegant way of determining an exhaustive list of sample elements in the sample space. It is by finding the ordered n-tuples of the elements in the events under consideration.
The tree diagram for selecting a person from the population in the given question can be found in the attached image below.
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Step-by-step explanation:
Answer:
b. As the sample size â increases, the variance of decreases. â So, the distribution of becomes highly concentrated around.
Step-by-step explanation:
Let : Yi,.... Yn are = i.i.d are random variables. The probability density of the distribution varies along with the sample size. When the sample size changes, the probability density of also changes.
The probability distribution may be defined as the statistical expression which defines the likelihood of any outcome for the discrete random variable and it can be opposed to the continuous random variable.
In the context, when the size of the sample of the distribution size increases, it causes a decrease in the variance and so the distribution becomes highly concentrated around.