Question: A major investment company wanted to know what proportions of investors bought stocks, bonds, both stocks and bonds, and neither stocks nor bonds. The company entrusted this task to its statistician, who, in turn, asked her assistant to conduct a telephone survey of 200 potential investors chosen at random. The assistant, however, was a moonlighter with some preconceptions of his own, and he cooked up the following results without actually doing a survey. For a sample of 200, he reported the following results:
Invested in stocks: 100
Invested in bonds: 75
Invested in both stocks and bonds: 45
Invested in neither: 90
The statistician saw these results and fired his moonlighting assistant. Why?