Rosemount High School, MN
Course Syllabus
A.P. Statistics
General Course Outline Prepared by Mike Floersch
Our High School math department currently utilizes the Chicago Series curriculum and texts, from Algebra through Pre-Calculus and Discrete Mathematics. The Advanced Placement Statistics course will be offered as an elective, with Algebra 2 as the prerequisite. Therefore, the students taking A.P. Stats will already have had an introduction to some of the topics of this course. This will allow some of the material to be covered as review while creating more time to cover the newer topics in more detail.
The following topics are the ones that the students should be familiar with upon completion of F.S.T.
Histograms Scatter plotsThroughout the course, the above topics will be reviewed as needed, however, the emphasis will be on the following:
interpreting the results of the dataThe following outline is modeled to fit the 3-Trimester school year.
The textbook used for this outline was Moore & McCabe's Introduction to the Practice of Statistics 2nd Ed. Obviously this is a tentative schedule and could change from trimester to trimester.
Trimester 1
Review data analysis
Plan a short survey to be given to all students in the school during home room. 15 - 20 questions. Sample questions: age, number of brothers & sisters, number of pets, amount of allowance each month...
The results of this survey will be used to create a large data base for the sole purpose of doing different comparisons. Later in the course it will be used to discuss bias, variance and sampling. This survey will also hopefully encourage ideas for their own experiments and studies.
Introduction to computer program for data analysis (probably Data Disk, for our Mac Labs). Learn basics of the program. Have students download the data collected form the surveys.
Discussion of Section 1.1 Displaying Distribution, choosing an appropriate display.
Assign selected problems from 1.1
Finish downloading data from survey if not already complete.
Using the data from the survey have the students chose three categories and for each one create a stem-leaf plot, a box plot, a histogram, and a pie chart. For each category identify which graph most appropriately displays the best information.
Assign more selected problems form 1.1
Emphasis on Resistant measures of spread, using calculators with tables capabilities to calculate standard deviation showing the steps, transformation of data, density curves, assessing normality.
1 day
review
1 day test
Looking at data : Relationships
3 days Scatter
plots, smoothing scatter plots
box plots (review)
categorical explanatory Variables
Use data from first day survey. Have students choose pairs of variables that
they think my be related.
Have students look up data: financial records or historical data to show examples that when smoothed, demonstrate a clearer relationship, and also have them propose explanations for the irregularities.
5 days
Computing regression using the formula for least squares regression line.
(students must become familiar with this formula)
Plotting residuals, interpreting these patterns.
Outliers and influential observations
Find data to compare: Almanacs, newspapers, etc.
3 days
Exponential growth, an application
Review exponential models, logarithms
Using the logarithm to transform exponential to linear
more residuals
3 days
Review correlation on graphing calculators, and its properties.
Become familiar with formula for correlation. Limitations, lurking
variables, review extrapolation & interpolation.
3 Days Categorical
data
Create bar graph from first day survey.
Find other data.
2 days
Causation Vs common response and confounding
Small project: Find an example from a news paper or journal study.
Determine if the proposed variables do indeed have a correlation,
and discuss causation.
2 days review
1 day test
Small project.
a. Using an almanac or journal, find data relating some variable to time (year, months, days, hours..). Create a scatter plot, use least squares regression to calculate a line and draw this on the graph. Discuss your results, especially the appearance of any outliers. If a linear fit is does not seem appropriate, explain why and test for quadratic fit.
b. Collect data from a current newspaper or magazine comparing to variables that may have a relationship. Again, make a scatter plot, do linear regression and discuss your conclusions.
c. Do a small survey (at least 15 data point) comparing two variables you belive may be related. Again, do a scatter plot, linear regression, and discuss your results. Is this study representative of a larger population? Explain why or why not.
Producing Data
.2 days First
steps
Need for design, sampling, experiments.
Have examples of numerous types of past studies.
Discuss design and procedures.
4 days
Design of experiments
Randomizing, causation, double blind, hidden bias, blocking
3 days
Sampling design
Simple random sampling, stratified random sampling
bias, other cautions
4 days Toward
Statistical Inference
Sampling distributions
Bias and Variability
Experiments, conclusions
Supplementary Assignment:
Have students bring in two examples of studies from each of the following
sources: Medical journal, news magazine, psychology journal, Social magazine
(People, Teen, etc..). Have the students analyze these different studies,
looking at method and design. Lead class discussions about the results: are they
valid? What populations are represented, is bias evident? If so, how? What could
be done to improve the results? Are these suggestions feezible?
small project
Design an experiment to answer the following question:
Is drinking soda pop (non-diet) related to weight gain?
Experiment does not have to be executed
Outline specifications, be very detailed
2 days Review
1 day test
Probability and Randomness
2 days Review probability, models, rules,
3 days Random
variables
Discrete, continuous, normal distributions
Quiz 4.1-4.2
3 days review
Chaps 1 - 4.2
Final exam
Trimester 2
5 days
Means., Variance and Random Variables
Describing Probability distributions
Mean of a Random Variable
Variance of a Random Variable
Law of Large numbers
Rules for means
Rules for variances
2 days Activities Use data from first day survey , from journals, and other sources to extimate population means on various sets of data. Discuss populations being represented.
2 days Review all of chapter 4
1 day test
Probability to Inference
3 days
Review binomial distribution, binomial coefficients, z-scores
Sample Proportions
Normal Approximation for Proportions and counts
3 days
Sample means, distribution
Central Limit Theorem
Use a couple sets of data to demonstrate on Data Disk.
3 days Control
charts
Out of Control Signals
2 days review
1 day test
Introduction to Inference
5 days
Estimating with confidence
Confidence intervals
critical values
Behavior of intervals
Discussions about common misconceptions and cautions
Examples from medical studies, and business records
5 days
Tests of significance
Null hypothesis, alternative hypothesis
P-values
levels of significance
z statistic, standard normal critical values
5 days Use and
abuse of tests
Identifying common errors
Analyze reports in the news, journals, etc.
Review 2 days
1 day testInference for Distributions
5 days Inference for the mean of a populationDepending upon number of days remaining in trimester, small or large project. Design an experiment or survey, comparing 2 variables. Use all appropriate tools to summarize findings.
3 days reviewFinal Exam
Begin looking at questions that may be similar to A. P. Exam. Including Multiple choice, free response and investigative.
Inference for Count Data
5 days Inference
for a single proportion
p-value
sample size
5 days Comparing
two proportions
Confidence intervals
Significance tests
pooled estimate
5 days
Inference for two way tables
Descriptive tables
models, hypothesis
r x c tables
expected counts
chi-square statistic
3 days review
1 day test
Inference for Regression
2 days
Review Linear Regression
Statistical Model for Linear regression
4 days
Estimating Regression Parameters
Confidence intervals and significance tests
Mean response, prediction intervals
Analysis of Variance
5 days Multiple
linear regression
Statistical Model
Estimation, confidence intervals, tests
2 days review
1 day test
Weeks 9 - 10 Review for A.P. Test (this time period will fluctuate each year as the date of the test alters)
Each day have the students work on examples of free response and investigative questions. Have them respond in detail, sharing results with the class. Allow the students opportunities to identify topics on which they want more practice time.
Weeks 11 - 12 Project
(Since the A.P. exam is over, the students need to have something to maintain their interest in the course. The following is designed to hopefully do this.)
With the students working in small groups, have them choose a topic of concern (drugs, alcohol, teen sexuality, ...) and propose a question about that topic. (example: Do high school athletes drink more or less alcohol than high school students who do not participate in athletics?) They must then do a large study (probably a survey) in an effort to answer their question. They may use the data form the survey at the beginning of the year as a starting point. They must carefully design the study, and outline all measures taken to minimize bias and error. This may be worked on during class time as well as on their own time. Results must be presented to the class as their final exam, and these results must show uses of z-statistics, t-tests, or other statistical measures appropriate to their study.
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