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Part 1: Answer the following questions in complete sentences and be ready for a test the first week of class. Chapter 1: What is the point? One important statistical practice is sampling. Explain the process of sampling and give an example that illustrates the process. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 2: Descriptive Statistics: Who was the best baseball player of all time? A descriptive statistic is a summary statistic that is very helpful in simplifying things. It’s easy to understand but is limited in what it can tell us. a) Give an example of a descriptive statistic. Explain the pros and cons of using the doing analysis. b) Descriptive statistics can be misleading. Describe how this is true in terms of mean and median. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 3: Deceptive Description: He’s got a great personality. a) The use of statistics to describe complex phenomena is not exact. There is a difference between “precision” and “accuracy”. These words are not interchangeable. Please explain the difference and give an example of how this difference can matter. b) Give an example of how using different units of analysis can present seemingly contradictory views. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 4: Correlation: How does Netflix know what movies I like? Correlation measures the degree to which two phenomena are related to each other. It is a number between 1 and 1 and it has no units attached to it. Correlation does not imply causation. Explain this statement and give an example that illustrates this concept. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 5: Basic Probability: Don’t buy the extended warranty. Probability is the study of events and outcomes involving an element of uncertainty. Probability can help determine in advance that some outcomes are more likely than others. It can also help tell us after the fact what likely did happen. Probability gives us tools for dealing with life’s uncertainties. Select one of the following statements and explain the event in terms of probability: a) You shouldn’t play the lottery. b) You should invest in the stock market if you have a long investment horizon. c) You should buy insurance for somethings, but not for others. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 5.5: The Monty Hall Problem. The “Monty Hall problem” is a famous probability-related conundrum faced by participants on the game show Let’s Make a Deal. Explain why you should switch doors. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 6: Problems with Probability: How overconfident math geeks nearly destroyed the global financial system. a) The underlying risks associated with financial markets are not as predictable as a coin flip or a blind taste test. Explain this statement in the context of the Value at Risk model (VaR). b) Give an example of problems that can happen when you either assume events are independent when they are not or not understanding when events are independent. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ _________________________________________________________________________________________ Chapter 7: The Importance of Data: Garbage in, garbage out. Data deserves respect. You need good data. No amount of fancy analysis can make up for fundamentally flawed data. One way to get data is from sampling. We need our sample data to be representative of some larger group or population. Some of the most egregious statistical mistakes involve lying with data; the statistical analysis is fine, but the data on which the calculations are performed are bogus or inappropriate. Hence the phrase garbage in, garbage out. Bias can be a contributing factor of bogus data. List a type of bias and explain how it affected the statistical results. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 8: The Central Limit Theorem: The Lebron James of statistics. The Central Limit Theorem is the “power source” for many of the statistical activities that involve using a sample to make inferences about a large population. The core principle underlying the central limit theorem is that a large, properly drawn sample, will resemble the population from which it is drawn. Obviously, there will be variations from sample to sample, but the probability that a sample will deviate massively from the underlying population is very low. Give an example of how the central limit theorem was applied. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 9) Inference: Why my statistics professor thought I might have cheated. The power of statistical inference derives from observing some pattern or outcome and then using probability to determine the most likely explanation for that outcome. Statistics cannot prove anything with certainty. Give an example of inference that depicts both its strengths and weaknesses. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 10: Polling: How we know that 64% of Americans support the death penalty (a sampling error of ± 3 %). The power of polling stems from the same source as the sampling examples: the central limit theorem. If we take a large, representative sample, we can reasonably assume that our sample will look a lot like the population from which it is drawn. The book listed key methodological questions that you should ask when conducting a poll, or when reviewing the work of others. Select one of the questions and explain its importance. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 11: Regression Analysis: The Miracle elixir. Regression analysis is the statistical tool that allows us to quantify the relationship between a particular variable and an outcome that we care about while controlling for other factors. In other words, it allows us to unravel complex relationships in which multiple factors affect some outcome that we care about. Give an example of regression analysis. State what the explanatory and dependent variables are. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 12) Common Regression Mistakes: The mandatory warning label. Regression analysis provides precise answers to complicated questions. These answers may or may not be accurate. In the wrong hands, regression analysis will yield results that are misleading or just plain wrong. Give an example that illustrates a potential regression pitfall and what caused it. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Chapter 13) Program Evaluation: Will going to Harvard change your life? Program evaluation is the process by which we seek to measure the causal effect of some intervention. The intervention that we care about is typically called the “treatment”. A treatment can be a literal treatment, as in some kind of medical intervention, or it can be something like attending college or receiving job training. Program evaluation offers a set of tools for isolating the treatment effect when cause and effect are otherwise elusive. The book talks about common approaches for isolating a treatment effect. Select one of the approaches and explain how it is effective in isolating a treatment effect. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ Part 2 The Essay: Five questions that statistics can help answer. The book posed five questions that statistics can help answer. Select one of the following questions and explain how statistics can help answer it. Question 1: What is the future of football? Question 2: What if anything is causing the dramatic rise in autism? Question 3: How can we identify and reward good teachers and schools? Question 4: What are the best tools for fighting global poverty? Question 5: Who gets to know what about you? Essay must be: 2 pages, typed and double spaced.