A wildlife biologist examines frogs for a genetic trait that is linked to sensitivity to an industrial toxin in the environment.
Suppose exposure to the toxin tends to increase the prevalence of the genetic trait in the population of frogs. Previous research has established that this trait is usually found in about 2/10 of all frogs in a `clean' environment. Suppose a location is suspected of contamination. A sample of 10 frogs are collected, then examined for the genetic trait. We are asked to interpret the data collected and determine whether there is evidence suggesting contamination. What is the fewest number of frogs in the sample with the trait (number of successes) for which we can conclude the area is contaminated?
Usually, when there is contamination the smallest amount can have huge ramifications in the data collected. In this scenario, if in a "clean" environment the trait is found in 2/10 frogs then anything above this number should be considered contaminated. This is because data above this ratio would be considered uncommon or rare and this unique occurrence can be most likely tied to the only new factor which would be the contamination. Therefore the minimum number of frogs with this trait in the sample would be 3.
