Creswell high school
Course syllabus
STATISTICS (with probability) 2016 – 2017
COURSE NUMBER: MTH 243
INSTRUCTOR: MR. SCOTT WORSHAM
CONTACT INFO: E-mail: sworsham@creswell.k12.or.us & Work Phone: 541-895-6031
OFFICE HOURS: 7:45 – 8:15 AM (Before School), 12:43-1:31 (Prep Period), & 3:15 – 3:45 (After School)
LENGTH: 1 YEAR
ROOM: 218 PREREQUISITES: ALGEBRA 2
TEXTBOOK: Stats-Modeling the World, AP edition, by Bock, Velleman and De Veaux,
Pearson – Addison Wesley, 2007
GENERAL COURSE DESCRIPTION:
Statistics is the art and science of collecting, organizing, analyzing, and drawing conclusions from data.
In Statistics, we will focus on four major themes:
- Exploring Data
- Sampling and Experimentation
- Anticipating Patterns
- Statistical Inference
Statistics is designed as the equivalent of a one-semester, introductory college statistics course. As a result of being a full year course, this high school course covers more topics in greater depth than any single “equivalent” college course.
In this course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance phenomena. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-83/84 graphing calculator, statistical software output, and Web-based java applets and activities to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.
Statistics is an advanced math class. You must put more time and effort into this math class then you have done in past years. If you feel that you will continue your educational growth into college, this course will also prepare you for that future endeavor.
COURSE GOALS:
- To help you become an educated consumer of data and statistical claims.
- To introduce you to the practice of doing statistics.
- To see the significance statistics has in other fields such as medicine, business, psychology, environmental science, sports, and other important fields.
- To help you be more prepared for a career and/or college
GRADING:
93 – 100 A 88 – 89 B+ 78 – 79 C+ 68 – 69 D+
83 – 87 B 73 – 77 C 63 – 67 D
90 – 92 A- 80 – 82 B- 70 – 72 C- 60 – 62 D- 0 – 59 F
QUIZZES / TESTS / INVESTIGATIVE TASKS 50%
(a) Quizzes will be taken at selected times during each Unit.
(b) Tests will be taken at the conclusion of each Unit.
(c) Investigative Tasks will be completed at the conclusion of most Chapters.
PROJECT 10%
There will be a Post Final Exam Project that will be used to summarize the course. The project will bring together all purposes of the course including designing an experiment, sampling, analysis, and drawing conclusions.
Note: All quizzes, tests, investigative tasks, and projects will be checked for evidence of correctly communicating methods, results, and interpretations using appropriate statistical vocabulary.
For PROJECTS based on data collection, a write up must include:
- Write, in words, not symbols, what the null and the alternative hypotheses are for you quest.
- In paragraph form, write how you designed the experiment. Make sure that you mention how you controlled for randomness, blocking, or lurking variables.
- Explain which statistical tests that you will use to test your hypotheses. Give an explanation why you chose the tests that you did and then tell what assumptions you had to make in order to use this test. Carry out the testing of your assumptions and explain if you can continue. If you fail to meet these assumptions, explain which one(s) failed. Carry out the tests anyway and in your conclusions discuss this. Remember to show the formulas used, the substitution step and the answers you got, p-values, etc.
- Based on the above information, state any conclusions that you can make. These conclusions should be several sentences long. You should include here an explanation of any problems you had that might have affected the outcome of your data or your conclusion.
- Explain to a prospective statistics student the meaning of your answer to the question.
HOMEWORK 20%
(a) Daily assignments need to be finished and complete before the next day of class.
(b) Late Homework turned in after the designated time on Turn-In Day will be penalized: 10% – 30% depending on the lateness of the work.
(c) All assignments will be checked for evidence of correctly communicating methods, results, and interpretations using appropriate statistical vocabulary.
FINAL EXAM 15%
WARM-UPS 5% (DAILY)
(a) Be in your seat working on the warm-up problems by the time the bell rings.
(b) Warm-ups will be collected once a month (after 10 – 20 school days)
TECHNOLOGY:
The graphing calculator offers you a variety of tools for entering, storing, sharing, displaying, analyzing, simulating and comparing sets of data. The World Wide Web offers interactive java applets, data sources, and sites with a variety of statistical information. We will even view a few video clips from the PBS series “Against All Odds: Inside Statistics” and “Decisions through Data” that were produced in the early 1990’s. Technology is an integral component of this class.
LCC Credit: Students are required to earn at least a 70% C- grade to earn Lane Community College Mathematics Credit.
ATTENDANCE:
Students must attend class regularly and be to class on time.
Tardy: Student’s arriving to class after the ‘start of class bell’ will be considered tardy. The third tardy in a grading period will result in an after school detention and every tardy thereafter.
Absent: Those students not in attendance or arriving later than 15 minutes into the class period will be considered absent. Students who have excused absences will be given extra time to complete missing assignments and make-up quizzes or tests.
Teaching Methods:
Students will gain valuable knowledge and learn from multiple approaches in class that include:
- Cooperative Learning
- Think-Pair-Share
- Modeling (I Do), Guided Practice (We Do), & Independent Practice (You Do)
- Differentiated Instruction (Objectives, Scaffolding, Visuals, Graphic Organizers, and etc.)
Class Discussion including some random question and answer sessions.
COURSE CONTENT TEXTBOOK
CORRELATION
UNIT 1: EXPLORING AND UNDERSTANDING DATA | 21 DAYS |
Displaying and Describing Categorical Data – Frequency Tables; the area principle; bar charts; pie charts; contingency tables; conditional distributions; segmented bar charts; Simpson’ paradox | SMW
CH. 3 |
Displaying Quantitative Data – Histograms; stem-and-leaf displays; dotplots; shape, center, and spread; comparing distributions; timeplots
Skill: Making a histogram on the calculator |
SMW
CH. 4 |
Describing Distributions Numerically – Median, IQR, and 5-number summary; making and comparing boxplots; mean and standard deviation; variability; determining which summary statistics to use when | SMW
CH. 5 |
The Normal Model – Standardizing with z-scores; how shifting and rescaling data effect shape, center, and spread; 68-95-99.7 rule; z-scores for percentiles; normal probability plots; assessing normality
Skill: Finding normal percentiles using the calculator |
SMW
CH. 6 |
UNIT 2: EXPLORING RELATIONSHIPS BETWEEN VARIABLES | 23 DAYS |
Scatterplots, association, and correlation – Describing scatterplots; explanatory vs. response variable; properties of correlation
Skill: Making a scatterplot using the calculator |
SMW
CH. 7 |
Linear Regression – The linear model; residuals; least squares regression line (LSRL); interpreting correlation; in context; Properties of the LSRL – b = r ∙ s, / ; () on LSRL
Skills: Calculator discovery of LSRL properties; computing residuals & making residual plots on the calculator |
SMW
CH. 8 |
Regression Wisdom – Subsets within data; prediction vs. extrapolation; outlier, leverage, and influential points; lurking variables and causation; summary values less variable than individual values | SMW
CH. 9 |
Re-expressing Data – Straightening relationships; goals of re-expression; the ladder of powers; power models – log x, log y transformations; exponential models – log y transformation; choosing the best model – residuals and
Skill: Transformation and regression models on the calculator |
SMW
CH. 10 |
UNIT 3: GATHERING DATA | 15 DAYS |
Understanding Randomness – Making and conducting simulations
Skill: Using random digits and using the calculator to help carry out simulations |
SMW
CH. 11 |
Obtaining Good Samples – Simple random sample (SRS); stratified sampling; cluster sampling, systematic sampling, multi-stage sampling
Sampling – sample size; census; populations and parameters vs. samples and statistics; sampling badly – voluntary response; convenience sampling; Designing and Implementing Surveys – Questions; wording, type, order; administration methods; response bias; undercoverage and nonresponse bias |
SMW
CH. 12 |
Experiments and Observational Studies – observational studies vs. randomized comparative experiments; s; control treatments; blinding; placebos; blocking; factors; confounding variables vs. lurking variables
Basics of Experimental Design – Subjects, factors, treatments, explanatory & response variables, placebo effect, blinding; completely randomized design (CRD); diagrams Principles of Experimental Design – control, random assignment, replication More Advanced Experimental Designs – Multi-factor experiments; block designs; why block?; difference between blocking and stratifying; matched pairs design |
SMW
CH. 13 |
UNIT 4: RANDOMNESS AND PROBABILITY | 17 DAYS |
Basic Probability Concepts – Probability as long-run relative frequency; randomness; legitimate probability models; sample spaces, outcomes, events; law of large numbers
Basic Probability Rules – Addition rule for disjoint events; complement rule; “something has to happen” rule |
SMW
CH. 14 |
Probability Rules – General addition rule, Venn diagrams, union and intersection; general multiplication rule, definition of independence; conditional probability, tree diagrams; disjoint vs. independent | SMW
CH. 15 |
Random Variables – Discrete vs. continuous;
Discrete Random Variables – expected value and standard deviation Rules for Means and Variances – linear transformations of a single variable, linear combinations of random variables, independence Continuous Random Variables – Combining normal random variables, calculating probabilities |
SMW
CH. 16 |
Binomial and Geometric Random Variables – Bernoulli trials; probability density function (pdf) vs. cumulative density function (cdf)
Geometric Distributions – X = # of trials up to and including 1^{st} success; calculating geometric probabilities; expected value of geometric random variable Binomial Distributions – X = # of successes; calculating binomial probability; finding mean and standard deviation for a binomial random variable Normal Approximation – Estimating binomial probabilities with normal calculations Skill: Geometric and Binomial distributions on the calculator |
SMW
CH. 17 |
UNIT 5: FROM THE DATA AT HAND TO THE WORLD AT LARGE | 17 DAYS |
Sampling Distribution Models – Moving towards inference; definition of sampling distribution; standard error
Sampling Distributions of – Mean and standard deviation of sampling distribution; normal approximation; assumptions and conditions – SRS, sample is < 10% of population, success/failure condition Sampling Distributions of – Mean and standard deviation of sampling distribution; Central Limit Theorem (CLT); assumptions and conditions – SRS, independence, 10% condition, large enough sample condition |
SMW
CH. 18 |
Confidence Intervals for Proportions – confidence intervals to estimate a population proportion, p
Estimating an Unknown Parameter – The idea of a confidence interval; connection with sampling distributions; margin of error; critical values Confidence Interval Considerations – Changing confidence level; interpreting Cl vs. interpreting confidence level; determining sample size; assumptions and conditions- independence, SRS, 10% condition, success/failure condition Skill: Calculate a one-proportion confidence interval on the calculator |
SMW
CH.19 |
Testing Hypothesis About Proportions – Significance tests with inference toolbox
Tests of Significance – Underlying logic of significance tests; stating hypotheses; one tailed vs. two-tailed tests; P-values vs. fixed significance levels; Skill: One proportion z-test on calculator |
SMW
CH. 20 |
More About Tests – Definition of “statistically significant”; significance level, critical value;
Type I & II Errors, Power – Type I & II error in context; connection between power and Type II error |
SMW
CH. 21 |
Estimating the Difference Between Population Proportions
Testing a Claim about the Difference Between Population Proportions – Using the pooled proportion as an estimate Skill: Two-proportion inference on the calculator |
SMW
CH. 22 |
UNIT 6: INFERENCE ABOUT POPULATION MEANS | 11 DAYS |
Statistical Inference for Mean – Describing sampling distributions of sample means using a model selected from the t-distributions based on degrees of freedom; variability in sample means is the standard error; margin of error for a confidence interval; testing hypotheses about population means; checking assumptions
Skill: Performing t procedures on the calculator |
SMW
CH.23 |
Statistical Inference to Compare the Means of Two Independent Groups – t-models; checking assumptions; standard error for the difference between two means; two-sample t intervals and two-sample t-tests
Skill: Performing two-sample t procedures on the calculator – different df |
SMW
CH. 24 |
Paired Samples and Blocks – Matched pairs vs. two independent samples | SMW
CH. 25 |
UNIT 7: INFERENCE WHEN VARIABLES ARE RELATED | 12 DAYS |
Chi-Square Goodness of Fit Test – The chi-square family of curves
Chi-Square Test of Homogeneity – Independent SRSs or randomized experiments Chi-Square Test of Association/Independence – Distinguishing between homogeneity and association/independence questions Activity: M&M color distributions |
SMW
CH. 26 |
Inference about Linear Regression – Population vs. sample regression lines
Confidence Intervals and Significance Tests about – Nasty formulas; computer output; abbreviated inference toolbox Skill: Regression inference on the calculator |
SMW
CH. 27 |
Hints & Suggestions
- Show Work – many answers in statistics are written in sentences and a one number answer value is usually not just the answer.
- If you come across a problem that’s giving you trouble, then you should:
(a) Look at your notes for help
(b) Look in the book for examples just like it
(c) Ask a fellow classmate for help
(d) Put a ? by it and ask later
- Do the REVIEW
- Stay up, not catch up. Turn Homework in on time!
- Always be ready to answer the warm-up problems.
Materials Needed : You are required to bring these materials to class every day.
1. Statistics Textbook 4. Paper or Notebook (to keep notes)
2. Warm-up Book 5. 3 Ringed Binder or Folder
- Mechanical Pencil with an eraser 6. TI-83/84 Graphing Calculator
You need a TI-83 or TI-84 Graphing Calculator to be successful in this class! Trust Me!
ACCESSIBILITY AND ACCOMMODATIONS:
It is Lane’s goal that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You may contact Disability Resources to discuss potential accommodations: (541) 463-5150 (voice); 711 (relay); Building 1, Room 218; or disabilityresources@lanecc.edu (e-mail). Please be aware that any accessible tables and chairs in this room should remain available for authorized students who find that standard classroom seating is not usable.