Human DNA Found In 66% Of Vegetarian Hot Dogs

[mahatmakanejeeves]

42. What percentage of the population of hot dogs is for vegetarians?

Last edited Tue Oct 27, 2015, 11:27 AM - Edit history (3)

That information is missing, certainly from the USA Today McStory. Is it 1%? 2%? 3%?

Let's say the samplers went out and bought 3,000 packages of hot dogs. What we have been told is that 2% of those 3,000 packages contained human DNA. That's 60 packages. Of those 60 packages, 40 were vegetarian products.

What I do not know is if vegetarian products are overrepresented in the contaminated group, underrepresented in the contaminated group, or on a par in the contaminated group. If you went out and bought 3,000 packages of hot dogs at random, how many of those would be vegetarian products?

Are vegetarian hot dogs more likely to contain human DNA than regular hot dogs, less likely to contain human DNA than regular hot dogs, or as likely to contain human DNA than regular hot dogs?

Let's say vegetarian hot dogs are 5% of the market. I don't know; I'm just making up numbers. Of the 3,000 packages of hot dogs the samplers buy, 5%, or 150, are vegetarian, and 95%, or 2,850, are regular. The testing finds 2% of the total population, or 60, are contaminated. 40 of those are vegetarian, and 20 are regular. In terms of percent, 40 out of 150 packages of vegetarian hotdogs, or 27% of them, are contaminated. 20 out of 2,850 packages of regular hot dogs, or 0.7%, are contaminated. That would make vegetarian hot dogs 38 times as likely as regular hot dogs to be contaminated.

Did I do that right? Outraged statisticians, please feel free to point out my errors (beyond the obvious one, pretending to be a statistician).

I doubt that vegetarian hot dogs constitute as much as 5% of the market. Juggle the assumptions around, and the numbers change.

Also, are the results being skewed by false positives? I recall the paradox of false positives on drug tests. Give me a few minutes, and I'll find an account. Here we go:

False positive paradox

The false positive paradox is a statistical result where false positive tests are more probable than true positive tests, occurring when the overall population has a low incidence of a condition and the incidence rate is lower than the false positive rate. The probability of a positive test result is determined not only by the accuracy of the test but by the characteristics of the sampled population. When the incidence, the proportion of those who have a given condition, is lower than the test's false positive rate, even tests that have a very low chance of giving a false positive in an individual case will give more false than true positives overall. So, in a society with very few infected people—fewer proportionately than the test gives false positives—there will actually be more who test positive for a disease incorrectly and don't have it than those who test positive accurately and do. The paradox has surprised many.