In employment discrimination cases courts have held that a

Question

1. M. S. Kanarek and associates studied the relationship between cancer rates and levels of asbestos in the drinking water, in 722 Census tracts around San Francico Bay. They tested over 200 relationships -- different types of cancer, different demographic groups, different ways of adjusting for possible confounding variables. After adjusting for age and socioeconomic status (but not smoking), they found a "strong relationship" between the rate of lung cancer among white males and the concentration of asbestos fibers in the drinking water: P<.001P<.001.

They found that a 100-fold increase in asbestos concentration was associated with a 1.05-fold increase in the lung cancer rate, on average. (This means: If tract B has 100 times the concentration of asbestos fibers in the water as tract A, and the lung cancer rate for white males in tract A is 1 per 1,000 persons per year, then tract B is predicted to have a rate of 1.05 per 1,000 persons per year.)

Are you convinced that asbestos in the drinking water causes lung cancer among white males? Please point to at least threedistinct flaws in this analysis.

2. In employment discrimination cases, courts have held that a firm is guilty of discrimination when the percentage of blacks among its employees is lower than the percentage of blacks in the surrounding geographical region, provided the difference is "statistically significant" (i.e., P-value less than 5%) by the z-test.

1. Suppose a firm is found guilty under this criterion. Why should you be skeptical? 
2. The difference may be statistically significant but not practically important
3. Data snooping makes P-values hard to interpret
4. The test is based on a sample of convenience
5. The test is based on data for the entire population
6. Consider a metropolitan area in which 10% of the people are black and 50 firms which hire employees independently by a process which, as far as race is concerned, is equivalent to simple random sampling. The chance that at least one of the 50 firms will be found guilty of discrimination is _____% and the expected number of firms that will be found guilty is ____.