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Case 4 Medical Results (10 Marks)
False positives (and negatives) are particularly an issue when it comes to medical testing and disease diagnoses. Laura’s doctor is concerned about her health and schedules her for some tests. She knows that the disease is fairly rare (only 1% of the population) ever contract it, but being a good doctor she wants to conduct a new test for the disease Laura may have.
If she has the disease, there is a 98% chance the test will be positive. If she doesn’t have the disease, there is 95% chance the test will be negative.
a) What percentage of the population will test positive?
b) If Laura tests positive for the disease, what is the probability she doesn’t actually have the disease?
c) If Laura tests negative for the disease, what is the probability she does actually have the disease?
d) What is the probability of the test being wrong?
Case 1: Diamonds (35 Marks)
Diamonds are categorized according to the “four C’s” Color, Clarity, Carat, and Cut. Each
diamond stone that is sold on the open market is provided a certificate by an independent
diamond assessor that lists these characteristics. For the period 2006 to 2010, ATC Diamond
Dealer collected the data for the first three C’s, data about diamond assessor and price ...
Case 2: (25 Marks)
In the file Survey Guelph.xls, you will find the responses (hypothetical) of over 200
questionnaires sent out by City of Guelph ...
Case 3: Matrix Wireless (30 Marks)
Part I (20 marks)
Matrix Wireless sells the BES smartphone with either the Bronze Standard Plan or the Silver
Standard Plan. Customers can later upgrade to the Gold Standard Plan. You have to analyze the
results of a market study that asked 5,000 Ottawa residents about whether they planned to
purchase the company’s BES smartphone over the next four months of 2015. The same 5,000
residents were surveyed two months later to find out if they had actually purchased the
company’s smartphone. The results are shown in the following table ...
Matrix Wireless-Part II (10 marks)
Matrix Wireless is also considering the introduction of a new smartphone, BTR. From past
experience, the probability of the introduction of a new smartphone being a success is 25%.
Before introducing the new smartphone, Matrix Wireless will hire York Research Associates
which will then issue a report that is either Favorable or Unfavorable. Historically, 80% of the
new smartphones that were introduced successfully received a favorable report, and 12% of the
new smartphones that were introduced unsuccessfully received a favorable report. For the new
smartphone, BTR, York Research Associates issued a favorable report. Should Matrix Wireless
introduce the new smartphone?
