M 362K, Spring 03, Smith

## Assignment for Wednesday, September 17

1. Read Section 3.3.
• Focus on p. 69, Examples 3a, 3c, 3d, 3f, and the middle of p. 75 - middle of p. 76.
• Note: The author of this textbook uses "odds" and "odds ratio" interchangeably. However, these terms are often used to refer to different (but related) concepts: "Odds" is usually used to refer to what is defined onp. 75 as odds ratio: The ratio of the probability of an event to the probability of its complement. "Odds ratio" is used when comparing the odds of something happening under two conditions -- thus, it is a ratio of odds. For example, the odds ratio of developing cancer when exposed to a certain chemical compared with not being exposed would be
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)?