M 362K, Spring 03, Smith

Assignment for Wednesday, September 17

1. Read Section 3.3.
Odds ratio = (Odds of developing cancer if exposed)/(Odds of developing cancer if not exposed)
Also,  phrases such as  "odds 3 to 2"are often used. In this case, "odds 3 to 2" means that the odds are 3/2.
2. Practice problems:
I. p. 106, #24.

II. If the odds of event A are 3 to 2 (see above), what is the probability of A? (Show your reasoning)

III. Some people develop severe allergies to rubber. There is concern that health care workers are especially vulnerable to this risk because they use latex gloves. In a study of this question, 177 subjects identified as health care workers were tested for latex specific IgE antibodies (a screening test for latex sensitivity).  Of these, 38 were found to be positive.  A total of 4228 non-health care workers were tested for this antigen and 827 of these individuals were positive. Assuming that the proportions in this study are representative of the population at large,

a)     Compute the odds of being positive for this antigen among health care workers.

b) Compute the odds of being positive among non-health care workers.

c) Compute the odds ratio (as defined above -- not as defined in the book) of being positive for health care workers compared to non-health care workers.

d) How could you do part (c) without first doing parts (a) and (b)?