Use Geogebra if need be :)

Studies have shown that sh can have distinct \"personalities\". Guppies are known to be \"schooling\" sh (that travel in groups and swim in coordinated directions), but individual guppies Show differences in how \"brave\" they are. While most guppies are very shy and jumpy, a subset of guppies show a \"brave\" personality type, and show less of a response to predators and are generally more curious. Previous research suggests that the proportion of brave guppies in the population is roughly p = .15, but you wish to know whether this proportion differs in particularly dangerous waters. (a) A sample of n = 200 guppies are collected from Danger Lake and tested to determine the number who are brave. 19 guppies demonstrate the brave personality type. Test the null hypothesis that the true population proportion 19 = .15 in Danger Lake. Use a signicance threshold of a = 0.05. State all relevant hypotheses (in symbols) and test statistics/ distributions, as well as the pvalue and appropriate conclusion of the test. (b) A researcher wishes to determine whether a population of guppies extracted from Danger Lake would exhibit a dierent population proportion of brave guppies after living for several generations in Peaceful Pond, a body of water with no predators. After a suitable amount of time has passed, samples of guppies from each of Peaceful Pond and Danger Lake are collected and compared. Test the null hypothesis that the population proportions of brave guppies are the same in these two populations. Use a signicance threshold of a = 0.05. State all relevant hypotheses (in symbols) and test statistics/ distributions, as well as the pvalue and appropriate conclusion of the test. Sample results: Danger Lake: N D L = 150, 15 brave. Peaceful Pond: N pp 2 210, 34 brave