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AP Statistics Summer Homework Welcome to AP Statistics!!! For you to be successful in the fall when you come back to school you will need to complete this summer homework assignment. This will be worth 4 grades when you get back to class in August. Each of the 3 parts will be worth its own grade and you will have an assessment over the knowledge covered in each part on the first day of school. I have broken the assignment down into pieces so you have a little to complete each month of summer. Please avoid doing all of the assignment at the one time the weekend before the first week of school. The assignment is designed to keep you brain active throughout the summer, not to do in two days.
Part One: June Book Study Read the book Naked Statistics: Stripping the Dread from Data by Charles Wheelan (ISBN: 978-0393347777)
There are short answer questions for each chapter. You need to answer in complete sentences with you own words.
Part 2: July Fundamental Skills Review There are several skills involved in AP Statistics that you have seen in the past, some of them have not been covered since middle school. Part 2 has mini lessons with practice for each of the skills you will be responsible for knowing on the first day of school. The content has been split into 2 categories data display and statistical measures. You must demonstrate mastery on these skills or you will be pulled for Mandatory Boot Camp the Second week of school.
Data Displays Statistical Measures Venn Diagrams Measures of Center Dot Plots Mean Absolute DeviationStem-and-Leaf Plots Standard DeviationHistograms Box-and-Whisker PlotScatter Plot
Part 3: August Vocabulary Crash Course Unit 1 is vocabulary heavy with 45 concepts that need to be mastered and will need to be applied in free response situations. Create vocabulary cards for each concept to use a reference during our first unit. I would suggest whole punching them and putting them on a ring or using spiral bound notecards in order to keep
them all together. Please reach out with any questions you have this summer, I am looking forward to having you in Statistics.
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Email: [email protected] Part 1: Answer the following questions in complete sentences to turn in the first day 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.
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.
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Chapter 10: Polling: How we know that 64% of Americans support the death penalty (a sampling errorof ± 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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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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.__________________________________________________________________________________________
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Part 2: July Fundamental Skills Review
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Part 3 August Vocabulary Crash Course
Vocabulary Terms
Create vocabulary cards for each concept to use a reference during our first unit. I would suggest whole punching them and putting them on a ring or using spiral bound notecards in order to keep them all together.
Definitions are from: “Stats: Modeling the World,” 3rd Edition, by Bock, Velleman, and De Veaux
Response Variable Values of the response variable record the results of each trial with respect to what we were interested in(In other words, the variable we are researching about a group of people.)
Population The entire group of individuals or instances about whom we hope to learn.
Parameter A numerically values attribute of a model for a population. We rarely know the true value of a population parameter, but we do hope to estimate it from sampled data. For example, the mean income of all employed people in the country is a population parameter.
Observational Study
A study based on data in which no treatments were assigned or no manipulation of factors has been employed.
Sampling Frame A list of individuals from whom the sample is drawn is called the sampling frame. Individuals who may be in the population of interest, but who are not in the sampling frame, cannot be included in any sample.
Sample A (representative) subset of a population, examined in hopes of learning about the population.
Representative A sample is said to be representative if the statistics computed from it accurately reflect the corresponding population parameters.
Census A sample that consists of the entire population is called a census.
Statistic Statistics are values calculated for sampled data. For example, the mean income of all employed people in a representative sample can provide a good estimate of the corresponding population parameter.
Sampling Variability
The natural tendency of randomly drawn samples to differ, one from another. This is not due to error but just the natural results of random sampling.
Sample Survey A study that asks questions of a sample drawn from some population in the hope of learning something about the entire population.
Randomization The best defense against bias is randomization, in which each individual is given a fair, random chance of selection.
Simple Random Sample
A simple random sample of a sample size n is a sample in which each set of n elements in the population has an equal chance of selection.
Stratified Random Sample
A sampling design in which the population is divided into several subpopulations, or strata, and random sample are then drawn from each stratum. If the strata are homogeneous (similar within the group), but are different from each other, a stratified sample may yield more consistent results than an SRS. Example: Grade Levels could serve as strata and you could select a random sample of 10 students from each grade level to be a part of your study.
Cluster Sampling A sampling design in which entire groups, or clusters, are chosen at random. Cluster sampling is usually selected as a matter of convenience, practicality, or cost. Each cluster should be representative of the population, so all the clusters should be heterogeneous and similar to each other.Example: At Southeast, Families could serve as clusters since they all have grade levels 6 – 12. You could randomly select 2 Families from the 18 at Southeast and use all members of those 2 Families to be a part of your study.
Multistage Sample Sampling schemes that combine several sampling methods are called multistage samples.Example: A national polling service may stratify the country by geographic regions, select a random sample of cities from each region (stratified), and then interview a cluster of residents in each city.
Systematic Sample A sample drawn by selecting individuals systematically from a sampling frame. When there is no relationship between the order of the sampling frame and the variables of interest, a systematic sample can be representative.Example: You have a roster of all 12th graders and randomly select every 5th 12th grade student to be a part of your study.
Convenience Sample
A convenience sample consists of the individuals who are conveniently available. Convenience samples often fail to be representative because every individual in the population is not equally convenient to sample.Example: Mall surveys
Bias Any systematic failure of a sampling methods to represent its population is bias.
Over-estimate The sample statistic is larger than the population parameter.
Under-estimate The sample statistic is smaller than the population parameter.
Voluntary Response Bias
Bias introduced to a sample when individuals can choose on their own whether to participate in the sample. Samples based on voluntary response are always invalid and cannot be recovered, no matter how large the sample
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size.People are more likely to response if they feel passionately about the subject matter, which will cause an over-estimate of the variable of interest.Example: Radio surveys
Undercoverage A sampling scheme that biases the sample in a way that gives a part of the population less representation than it has in the population suffers from undercoverage.Example: You only take a random sample of 12th graders from Mrs. Rayburn’s AP English Language classes and do not include Mr. Hennessey’s AP English Language classes.
Non-Response Bias Bias introduced when a large fraction of those samples fails to respond. Those who do respond are likely to not represent that entire population. Voluntary response bias is a form of non-response bias, but non-response may occur for other reasons. Example: Those who are at work during the day may not respond to a telephone survey conducted by calling them during working hours only.
Response Bias Anything in a survey design that influences responses falls under the heading of response bias. One typical response bias arises from the wording of questions, which may suggest a favored response. Example: Voter are more likely to express support for “The President” than support the particular person holding that office at the moment.
Experiment An experiment manipulates factor level to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject groups across treatment levels.
Experimental Units Individuals on whom an experiment in performed. Usually called subjects or participants when they are human.
Random Assignment
To be valid, an experiment must assign experimental units to treatment groups at random.
Factor A variable whose levels are manipulated by the experimenter. Experiments attempt to discover the effect that different in factor levels may have on the responses of the experimental units.Example: Diet and exercise can help people lose weight. These are both factors of an experiment.
Level The specific values that the experimenter choose for a factor are called the levels of the factor.Example: Diet and exercise can help people lose weight. For the factor “diet” we could have 2 levels: strict diet and no diet restrictions. For the factor “exercise” we could have 2 levels: exercise and no exercise.
Treatments The process, intervention, or other controlled circumstances applied to randomly assigned experimental units. Treatments are the different levels of a single factor or are made up of combinations of levels of two or more factors.Example: Diet and exercise can help people lose weight. We could have 4 treatments: (1) Strict diet and exercise, (2) strict diet and no exercise, (3) no diet restrictions and exercise, and (4) no diet restrictions and no exercise.
Response A variable whose values are compared across different treatments. Example: Diet and exercise can help people lose weight. After the treatment plans are over, our response variable would be how much weight each person lost over the time they were on the treatment plan.
Cause-and-Effect In a randomized experiment, large response differences can be attributed to the effect of the differences in treatment level.The treatment caused the differences in the response variable.
Confounding When the levels of one factor are associated with the levels of another factor in such a way that their effects cannot be separated, we say these two factors are confounded
Control Group The experimental units assigned to a baseline treatment level, typically either the default treatment, which is well understood (like a current drug), or a null/placebo treatment. Their response provide a basis for comparison.Example: Our “no diet restriction and no exercise” group would be considered a control group.
Placebo A treatment known to have no effect, administered so that all groups experience the same conditions. Many subjects respond to such a treatment (a response known as a placebo effect). Only by comparing with a placebo can we be sure that the effect of a treatment is not due simply to the placebo effect.
Placebo Effect The tendency of many human subjects (often 20% or more of experiment subjects) to show a response even when administered a placebo.
Blinding Any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups is said to be blinded.There are two main classes of individuals who can affect the outcome of an experiment:
- those who could influence the results (subjects, treatment administrators, etc.)- those who evaluate the results (judges, evaluating physicians, etc.)
Single-Blind When every individual in either of the above classes is blinded, an experiment is said to be single-blind.
Double-Blind When everyone in both classes is blinded, we call the experiment double-blind.
Principles of Experimental Design
- Control aspects of the experiment that we know may have an effect on the response, but that are not the factors being studied
- Randomize subjects to treatments to even out effects that we cannot control
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- Replicate over as many subjects are possible- Block to reduce the effects of identifiable attributes of the subjects that cannot be controlled
Statistically Significant
When an observed difference is too large for us to believe that it is likely to have occurred naturally, we consider the difference to be statistically significant.
Completely Randomized Design
In a completely randomized design, all experimental units have an equal chance of receiving any treatment.
Blocked Experimental Design
When groups of experimental units are similar, it is often a good idea to gather them together into blocks. By blocking, we isolate the variability attributable to the difference between the blocks so that we can see the differences caused by the treatments more clearly. In a randomized block design, the randomization occurs only within blocks.
Matched Pairs Design
Subjects who are similar in ways not under study may be matched and then compared with each other on the variables of interest. Matching, like blocking, reduces unwanted variation. Matching is similar to blocking, with blocks being of size 2. You can also use a matched pairs design if the experimental unit or subject has the ability to receive both treatments and you can compare the experimental unit or subject to itself.
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