 Statistics & Probability Questions

Subject Mathematics General Statistics

Question

Answer the following questions:

1 – Consider a breast cancer screening test with a sensitivity of 95%, and a specificity of 95% applied to a sample of 10,000 subjects. As of 2005, there were an estimated 2.521 million cases of breast cancer in the US population of approximately 295.560 million. Calculate
(a) The expected number of false positives in the given sample.
(b) The expected number of false negatives in the given sample.
(c) The PPV
(d) The NPV
(e) The accuracy of the test
2 - A dominantly inherited genetic disease is identified over several generations of a large family. However, about half of families have dominant disease with complete penetrance, whereby if a parent is affected, there is a 50% probability that any one offspring will be affected. Similarly, about half of families have dominant disease with reduced penetrance, whereby if a parent is affected; there is a 25% probability that any one offspring is affected. Suppose in a particular family one parent and two out of two offspring are affected. What s the probability that exactly two out of two offspring will be affected in a family with dominant disease with complete penetrance?
3 - What is the probability that exactly two out of two offspring will be affected in a family with dominant disease with reduced penetrance?
4 - What is the probability that the mode of transmission for this particular family is dominant with complete prenetrance? Is this a prior or a posterior probability?

Solution Preview

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1) In order to fill out the “diagnostic matrix” below, we apply the percentage of people diagnosed with breast cancer via the screening test to give the number with and without breast cancer (85 and 9915). The sensitivity percentage is used to find those with breast cancer and a positive or negative screening. The specificity percentage is used to find those without breast cancer and a positive or negative screening.

Breast Cancer No Breast Cancer Total
Positive Screening           81                   496             577
Negative Screening          4                    9419           9423
Total                                   85                   9915          10000...

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