College couples are now asking for AIDS test The cold facts about the ``Hot Hand" in basketball The best NFL field goal kickers: are they lucky or good?
1. In one of Marilyn vos Savant's columns in Parade Magazine the following question was asked.
Suppose we assume that 5%of the people are drug-users. A test is 95 accurate, which we'll say means that if a person is a user, the result is positive 95 of the time; and if she or he isn't, it's negative 95%of the time. A randomly chosen person tests positive. Is the individual highly likely to be a drug-user?
Marilyn's answer was:
Given your conditions, once the person has tested positive, you may as well flip a coin to determine whether she or he is a drug-user. The chances are only 50-50.
How can Marilyn's answer be correct?
2. An article in Monday's New York Times reported that college students are beginning to routinely ask to be tested for the AIDS virus.
The standard test for the HIV virus is the Elias test that tests for the presence of HIV antibodies. It is estimated that this test has a 99.8%sensitivity and a 99.8%specificity. 99.8%specificity means that, in a large scale screening test, for every 1000 people tested who do not have the virus we can expect 998 people to have a negative test and 2 to have a false positive test. 99.8%sensitivity means that for every 1000 people tested who have the virus we can expect 998 to test positive and 2 to have a false negative test.
The Times article remarks that it is estimated that about 2 in every 1000 college students have the HIV virus. Assume that a large group of randomly chosen college students, say 100,000, are tested by the Elias test. If a student tests positive, what is the chance this student has the HIV virus? What would this probability be for a population at high risk where 5%of the population has the HIV virus?
If a person tests positive on an Elias test, then two more Elias tests are carried out. If either is positive then one more confirmatory test, called the Western blot test, is carried out. If this is positive the person is assumed to have the HIV virus. In calculating the probability that a person who tests positive on the set of four tests has the disease, is it reasonable to assume that these four tests are independent chance experiments?
This assignment is for the next two weeks to be handed in with your journals on Thursday 21 October. As usual, do no leave this work until the last minute as we will be using the material covered in our work in class.
Read Chapters 3,4 , and 5 of FPPA. Do the following exercises:Review Exercises in Chapter 4: page 70: #2, 4, 8, 9, 11, 12Review Exercises in Chapter 5: page 87: #4, 7, 8, 9,12
(1) Read the two articles on streaks in basketball and kickers in the National Football League and record your first impressions of these results in you journals. We will talk about them in some detail later.
(2) Find the article on gopher written by Mark Stein for the LA Times on the ``evil twin strategy" for football pools. This is a rather technical topic for a science writer to get straight. Can you understand the evil twin strategy from his write-up. Did he make any obvious mistakes?
Simpson's Paradox: As the discussion in the x-hour yesterday showed, it is not really easy to explain why Simpson's paradox occurs in real life situations. There have been several articles written on real life situations where this paradox occurs but these articles are often written for people quite familiar with statistics. It would be very useful to have a discussion of this paradox that is aimed at a non-technical audience and explains how the paradox can occur using real life examples.
Gun control: Different states in the U.S. and different countries have different laws regarding gun control. Can you determine from statistical evidence of the number of homicides etc., the effectiveness of gun control?
The Evil Twin strategy: Based on the success of Prosser and Snell employing the evil twin strategy in the math department football pool, another pair has decided to employ this strategy. How will this effect the winnings of Prosser and Snell?