1. A biologist is studying fish diversity Lake Erie. The biologist knows that Black Carp are an invasive species in the region and would like to estimate the proportion of fish in Lake Erie that are Black Carp. Of 250 randomly sampled fish from Lake Erie, the biologist catches 120 Black Carp. What is the margin of error for a 95% confidence interval for the true proportion of fish that are Black Carp in Lake Erie?
2. The biologist then moves on to studying fish biodiversity in Lake Huron, and again would like to estimate the proportion of fish in Lake Huron that are Black Carp. Of 112 randomly sampled fish from Lake Huron, the biologist catches 109 Black Carp. What is the upper bound for a 90% confidence interval for the true proportion of fish that are Black Carp in Lake Huron?
3. The biologist is studying Black Carp invasiveness in Lake Ontario next. He doesn't have time to sample the fish himself, so instead he instead asks a fisherman who has been fishing off of one of Toronto's piers all morning about his catch. The fisherman responds that, of the 75 fish he has caught, 55 have been Black Carp. What is the lower bound of a 99% confidence interval for the true proportion of fish that are Black Carp in Lake Ontario?