(a) A sample of n = 120 guppies are collected from Danger Lake and tested to determine the number who are brave. 10 guppies demonstrate the brave personality type. Test

the null hypothesis that the true population proportion is p = .15 in Danger Lake.Use a significance threshold of a = 0.05. State all relevant hypotheses (i symbols)and test statistics/distributions, as well as the p-value and appropriate conclusion of the test. You may use geogebra to help out with computations for this problem. 6. Studies have shown that fish can have distinct "personalities". Guppies are known to be" schooling" fish (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. (b) A researcher wishes to determine whether a population of guppies extracted from Danger Lake would exhibit a different 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 significance threshold of a = 0.05. State all relevant hypotheses (in symbols) and test statistics/distributions, as well as the p-value and appropriate conclusion of the test. You may use geogebra to help out with computations for this problem.