Review of 2009-2010 Program
Biology research projects:
Module 1: Is the lake safe to swim in?
If you pay attention to the news, every summer you will hear reports of beaches in Minnesota being closed due to unsafe levels of bacteria in the water. In this project, you will learn how scientists monitor water for bacteria, and how bacteria are identified by doing a variety of tests including DNA fingerprinting. Ultimately, you will be testing a local body of water to monitor for levels of bacteria.
Module 2: Finding Friends in the Field and Forest
This module will include an exploration of techniques and procedures used to design field experiments to further study plant biology, animal biology, and ecological concepts. Students will conduct analyses of the interrelatedness of the living and non-living factors in the environment, as well as taxonomic studies and surveys of the plant, bird, mammal, and insect species in Minnesota. Projects will be field oriented and will require students to collect data in the field. Students will study habitat diversity and quality in local environments looking at birds, mammals, insects, aquatic life, or plants.
Math research projects:
Module 1: Just When You Think You Have it All Figured out - Hypothesis Testing Proves You Wrong!
There are two types of statistical inferences: estimation of population parameters and hypothesis testing. Hypothesis testing is one of the most important tools of application of statistics to real life problems. Most often, decisions are required to be made concerning populations on the basis of sample information. Statistical tests are used in arriving at these decisions. There are five ingredients to any statistical test:
(a) Null Hypothesis
(b) Alternate Hypothesis
(c) Test Statistic
(d) Rejection/Critical Region
In attempting to reach a decision, it is useful to make an educated guess or assumption about the population involved, such as the type of distribution. In this module, you will research a topic that you've always felt strongly about one way or the other and would like to find concrete information on. It may be a burning question that you would like to find a "Yes" or "No" answer to, or it may be a topic that you would love to have more statistical data on. Whatever the case may be, this summer you will delve into your area of choice and, after researching it, you will perform Hypothesis Testing on the topic and make invaluable conclusions at the end.
Module 2: Probability - Making Informed Decisions by Playing to Win
Uncertainty and partial information - that is what we face every day when we try to make informed decisions. Probability is another one of the important tools in solving real life problems. Often we have to estimate the chance of various outcomes and then make a choice to maximize gain or minimize loss. A study of probability involves:
(a) determining the sample space, or set of possible outcomes
(b) assigning probabilities to outcomes based upon past observations (empirical probability) or a hypothesis of what should happen (theoretical probability)
(c) calculating the likelihood of various events using the laws of probability
(d) making an informed decision
In this module you will investigate probability from the perspective of game playing. You will determine whether a game is fair. You will determine the likelihood of events in the game. You will use probability to develop good strategies to win the game. And you will apply these principles of probability to everyday decision making - including trying to predict the weather. This module will provide even more tools for investigating your research topic.
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