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AP Statistics Syllabus
Teacher Information: Mr. Hendricks
Room #: 252
Phone: (262) 626-8427 ext. 4252
Content Topics and Essential Learnings
Exploring Data (These topics need to be understood before the semester begins!!)
- Identifying individuals and variables in a set of data.
- Identifying each variable as categorical or quantitative.
- Making bar graphs and pie charts of the distribution of a categorical variable.
- Interpreting the results of the bar graph or pie chart.
- Making dot plots of the distribution of a small set of observations.
- Making stem plots of the distribution of a quantitative variable, rounding leaves or split stems as needed.
- Making histograms of the distributions of quantitative variables.
- Making and interpreting ogives of sets of quantitative data.
- Looking for the overall patterns and major deviations from the pattern.
- Determine from the above graphical displays whether the shape of the distribution is roughly symmetric, skewed, or neither.
- Discuss the overall pattern by giving the numerical measures of center and spread in addition to a verbal description.
- Determine which measure of center and spread are more appropriate: the mean and standard deviation or the five-number summary.
- Recognize outliers.
- Making time plots of data, with the time of each observation on the horizontal axis and the value of the observed variable on the vertical axis.
- Recognizing strong trends or other patterns in time plots.
- Finding the mean and median of a set of observations.
- Recognizing what it means to be resistant and that skewness in a distribution moves the mean away from the median toward the long trial.
- Finding the quartiles for a set of observations.
- Giving the 5-number summary and drawing box plots.
- Finding the standard deviation for a set of observations. Also knowing the basic properties of the standard deviation.
- Determining the effect of linear transformations on the center and spread. Using side-by-side graphs to compare distributions of categorical data. Also being about the write narrative comparisons using the shape, center, spread, and outliers between two or more quantitative distributions.
Normal Distributions (These topics need to be understood before the semester begins!!)
- Knowing the properties of a density curve
- Locating the mean and median on a density curve and interpret what they do on that curve.
- Know how the mean and median change with symmetric and skewed density curves.
- Recognizing the shape of normal curves and being able to estimate the mean and standard deviation from the curve.
- Using the 68-95-99.7 rule and symmetry to state what percent of the observations from a normal distribution fall between two points when both points lie at the mean or one, two, or three standard deviations on either side of the mean.
- Finding the z-score of an observations and being able to interpret what it means.
- Given that a variable has a normal distribution with a stated mean and standard deviation, find the proportion of values above, below, or between stated numbers.
- Given that a variable has a normal distribution with a stated mean and standard deviation, calculate the point having a stated proportion of all values above or below it.
- Plot histogram, stem plot, or box plot to see if a distribution is approximately normal.
- Determine the proportion of observations within one, two, and three standard deviations of the mean and use the 68-95-99.7 rule to check if a distribution is normal.
- Construct and interpret normal probability plots.
Examining Relationships
- Identifying each variable as categorical or quantitative
- Identifying the explanatory and response variables in situations where one variable influences another.
- Making scatter plots to display relationships between two quantitative variables.
- Adding categorical variables to scatter plots.
- Describing the form, direction, and strength of the overall pattern of a scatter plot.
- Finding correlation between two quantitative variables.
- Knowing the basic properties of correlation.
- Explaining what the slope and intercept mean in the regression equation.
- Finding the least squares regression line equation.
- Find the slope and intercept from the means and standard deviation of x and y along with their correlation.
- Use the regression line to predict y for a given x. Being able to recognize extrapolation.
- Find and interpret it.
- Recognize influential observations and outliers in a scatter plot.
- Calculate and interpret residuals.
- Making residual plots and interpreting them.
- LRSL Project
More on Two-Variable Data
- Recognizing when there is exponential growth and decay
- Recognizing power functions.
- Performing logarithmic transformations and least squares regression on non-linear data.
- Performing inverse transformations to produce an equation for the original data.
- Interpreting correlation and LSRL and how they are influenced by extreme observations.
- Recognizing lurking variables.
- Finding marginal distributions and describing relationships between variables from them.
Producing Data
· Identifying the population in a sampling distribution.
· Recognizing the types of bias in sampling.
· Using Table B of random digits to select simple random samples from a population.
· Recognizing under coverage and non-response along with how wording of questions can affect responses.
· Use random digits to select stratified random samples from a population.
· Recognize the difference between an observational study and an experiment.
· Recognize bias due to confounding in studies.
· Identify the factors, treatments, response variables, and experimental units in an experiment.
· Outline a design of a completely randomized experiment. This design should show the sizes of groups, the specific treatments, and the response variable.
· Recognize when double-blind techniques should be used and what the placebo effect is.
· Know what block design and matched pairs design are and is and when it should be used.
· Be able to run and explain simulations.
Probability
· Describe the sample space of a random phenomenon.
· Be able to use the probability rules and apply them.
· Use Venn diagrams, Tree diagrams, and counting principles to find probabilities.
· Determine if two events are disjoint, complementary, or independent. Find unions and intersections of two or more events.
· Understand the idea of conditional probability and be able to find them.
· Construct tree diagrams to organize the use of the multiplication and addition rules with several stages.
Random Variables
· Be able to recognize and define a discrete random variable.
· Be able to construct a probability distribution table and probability histogram for a random variable.
· Be able to recognize and define a continuous random variable.
· Be able to determine probabilities of events as areas under density curves.
· Given a normal random variable, be able to use the standard normal table or a graphing calculator to find probabilities of events as areas under the standard normal distribution curve.
· Calculate the mean and variance of a discrete random variable. Find the expected payout in a game of chance.
· Use the law of law numbers to approximate the mean of a distribution.
· Use the rules for means and variances to solve problems involving sums, differences, and linear combinations of random variables.
Mid-Term Exam
Binomial and Geometric Distributions
· Identify a random variable as binomial by verifying the conditions.
- Use a TI-83 or the formula to determine binomial probabilities and to construct probability distribution tables and histograms.
- Calculate cumulative distribution functions for binomial random variables. Be able to construct cdf tables and histograms.
- Calculate means and standard deviations of binomial random variables.
- Use a normal approximation to the binomial distribution to compute probabilities.
· Identify a random variable as geometric by verifying the conditions.
- Use a TI-83 or the formula to determine geometric probabilities and to construct probability distribution tables and histograms.
- Calculate cumulative distribution functions for geometric random variables. Be able to construct cdf tables and histograms.
- Calculate means and standard deviations of geometric random variables.
Sampling Distributions
- Identify parameters and statistics in a sample or experiment.
- Recognize the fact of sampling variability.
- Interpret sampling distributions by describing a statistic in all possible repetitions of a sample or experiment under the same conditions.
- Describe the bias and variability of a statistic in terms of the mean and spread of its sampling distribution.
- Recognize when a problem involves a sample proportion .
- Find the mean and standard deviation of the sampling distribution of a sample proportion for an SRS of size n from a population having population proportion .
- Know when you can use a normal approximation to the sampling distribution of .
- Recognize when a problem involves the mean of a sample.
- Find the mean and standard deviation of the sampling distribution of a sample meanfrom an SRS of size n when the mean and standard deviation of the population are known.
- Know what happens to the standard deviation when the sample size gets larger or smaller for both sample proportions and sample means.
- Understand that has approximately a normal distribution when the sample is large.
- Use the normal approximation to calculate probabilities that concern and .
Introduction to Inference
- State in your own words what “95% confidence” or other statements of confidence in statistical reports means.
- Calculate a confidence interval for the mean of a normal population with known standard deviation.
- Recognize when you can use the procedure for a confidence interval.
- Know how the CI changes with a different sample size and level of confidence.
- Be able to find the sample size required to obtain a confidence interval of specified margin of error when the confidence level and other information are given.
- State the null and alternative hypotheses in a testing situation when the parameter in question is a population mean .
- Explain in your own words the meaning of the P-value.
- Calculate the one-sample statistic and the P-value for both one-sided and two-sided tests about the mean of a normal population.
- Assess statistical significance at standard levels , either by comparing P to or by comparing z to standard normal critical values.
- Recognize that significance testing does not measure the size or importance of an effect.
- Explain what type I error, type II, and power are in a significance-testing problem.
Inference for Distributions
· Recognize when a problem requires inference about a mean or comparing two means.
· Recognize from the design of a study whether one ample, matched pairs, or two sample procedures are needed.
· Use the t procedures to obtain a confidence interval at a stated level of confidence for the meanof a population.
· Carry out a t test for the hypothesis that a population mean has a specified value against either a one-sided or a two-sided alternative.
· Recognize when t procedures are appropriate in practice and when the procedures will be risky to use.
· Recognize matched pairs data and use t procedures to obtain confidence intervals and to perform tests of significance.
· Give a confidence interval for the difference between two means.
· Test the hypothesis that two populations have equal means against either a one-sided or a two-sided alternative.
· Recognize when the two-sample t procedures are appropriate in practice.
Inference for Proportions
- Recognize from the design or study whether one-sample, matched pairs, or two-sample procedures are needed.
- Recognize what parameter or parameters an inference problem concerns.
- Calculate the sample proportion or proportions from the sample counts.
- Use the z procedure to give a confidence interval for a population proportion.
- Use the z statistic to carry out a test of significance for the hypothesis about a population proportion against either a one-sided or two-sided alternative.
- Use the two-sample z procedure to give a confidence interval for the difference between proportions in two populations based on independent samples from the populations.
- Use a z statistic to test the hypothesis that proportions in two distinct populations are equal.
- Check that you can use both one proportion and two proportion z procedures by making sure that all of the conditions work in a particular setting.
Inference for Tables
- Use percents and bar graphs to compare hypothesized and actual distributions.
- Distinguish between tests or homogeneity of populations and tests of association/independence.
- Organize categorical data in a two-way table. Then use percents and bar graphs to describe the relationship between the categorical variables.
- Explain what null hypothesis is being tested.
- Calculate expected counts.
- Calculate the component of the chi-squared statistic for one cell as well as the overall statistic.
- Give the degrees of freedom of a chi-squared statistic.
- Use the chi-square critical values in Table E to approximate the P-value of a chi-squared test.
- Locate expected cell counts, the chi-square statistic, and its P value on a calculator.
- Use the chi-squared components to see what deviations from the null hypothesis are most important when the test is significant.
Inference for Regression
- Make a scatterplot to show the relationship between an explanatory and a response variable.
- Use a calculator to find the correlation and the least squares regression line.
- Recognize the regression setting
- Recognize which type of inference you need in a particular regression setting.
- Know when inference isn’t safe.
- Explain the meaning of the slop of the true regression.
- Using the output of the regression, find the slope and intercept of the LSRL, their standard errors, and the standard error about the line.
- Carry out the tests and calculate confidence intervals for .
- Explain the difference between a confidence interval for the mean response and a prediction interval for an individual response.
Review for AP Exam and Final Exam
Course Materials
Text: Yates, Daniel S., Moore, David S., and Starnes, Daren S. The Practice of Statistics. New York: W.H. Freeman, 2002.
Student Supplies
Pencils & Erasers
Spiral Bound Notebook
A graphing calculator (i.e. TI-83, TI-83 Plus, TI-84, or TI-84 Plus)
Folder
Binder for portfolio
District polices
Assignments, Tests, Quizzes, and Portfolios
Assignments will be given at the end of each class session. These assignments are expected to be completed by the next class session. There will be weekly homework quizzes where you will be assessed on the material from that week. Any topics covered by the homework can be on the unit exam.
· Do homework neatly, on loose-leaf paper, using a pencil.
· Show your work! This means all equations and every step!
· Extra help is available; all you have to do is ask.
Exams will be given at the end of each unit of study. Use a pencil to complete.
- Cheating will not be tolerated and result in you having to retake the exam before or after school. A call home will also be issued and an extra review assignment will have to be completed before the exam can be retaken. If you are talking or distracting others while they are taking a test or quiz, you will be considered cheating.
- It is required that you will achieve 80% or above on each exam. If you do not achieve this you will have to come in for tutoring to achieve this goal. Any student will have the option of retaking any exam throughout the quarter.
A mid-semester final exam and semester final exam will be given. Use pencil to complete.
A Portfolio that includes your journal entries will be compiled throughout the school year. This is a reflection of what you have achieved throughout the semester. This will be graded twice during the semester.
Course Evaluation
Grading Scale
A+ 100% A 95 – 99% A- 93 –94%
B+ 90 – 92% B 87 – 89% B- 85 – 86%
C+ 82 – 84% C 79 – 81% C- 77 – 78%
D+ 75 – 76% D 72 – 74% D- 70 – 71%
F Below 70%
Grading Breakdown
Projects, Homework Quizzes, & Portfolio 20%
Chapter Tests 65%
Exam 15%
Classroom Rules
Always respect others. This includes their belongings, their bodies, and what they have to say (includes gossip, cursing/swearing, teasing, etc.)
Follow directions the first time they are given. This keeps the class from wasting time, which gives you more time to work on your homework and get answers to your questions.
Raise your hand and wait for permission to speak or leave your seat. The only reason that you should leave your seat without permission is in an emergency.
Be in your seat and working when the bell rings. The bell does not start or end class, you do. If class starts late, expect it to end late. If you are tardy to class (not in your seat when the bell rings), the following apply:
1st tardy – warning 2nd tardy – warning 3rd tardy– detention
Each tardy thereafter – detention and a call home
Be prepared for class. This means they are to bring all required course materials to class each day. No hall passes will be given during the class period, you will have to use the 8 minutes before or after class.
If you choose to break a rule:
1st time: verbal warning
2nd time: 1 minute after class with me
3rd time: 20 minutes before or after school with me* and the completing of an Action Plan.
4th time Removal from the classroom, an individual conference with me, and a call home.
Severe Clause: You will immediately be sent down to the office.
*Failure to serve detentions with me within 5 days will result in having to serve them with the office, which doubles the time (40 minutes).
Technology
Your graphing calculator is a tool for using in the classroom and on your homework, not a toy. No games should be on it. If you are caught playing games on your calculator during class, I shall confiscate the calculator and remove the game program(s). Additionally, your parents shall be notified since this will be viewed as inappropriate behavior, insubordination, and classroom misconduct. I realize a calculator is expensive, however it should be viewed as an investment since you will be able to use it for the years you are at Kewaskum High School and during your college career. Please be sure to put your name on it so it is easily identified as yours.
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