Syllabus

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:

 

  1. Exploring Data
  2. Sampling and Experimentation
  3. Anticipating Patterns
  4. 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:

 

  1. To help you become an educated consumer of data and statistical claims.
  2. To introduce you to the practice of doing statistics.
  3. To see the significance statistics has in other fields such as medicine, business, psychology, environmental science, sports, and other important fields.
  4. 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:

  1. Cooperative Learning
  2. Think-Pair-Share
  3. Modeling (I Do), Guided Practice (We Do), & Independent Practice (You Do)
  4. 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 DataFrequency Tables; the area principle; bar charts; pie charts; contingency tables; conditional distributions; segmented bar charts; Simpson’ paradox SMW

CH. 3

Displaying Quantitative DataHistograms; stem-and-leaf displays; dotplots; shape, center, and spread; comparing distributions; timeplots

Skill: Making a histogram on the calculator

SMW

CH. 4

Describing Distributions NumericallyMedian, 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 ModelStandardizing 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 correlationDescribing scatterplots; explanatory vs. response variable; properties of correlation

Skill: Making a scatterplot using the calculator

SMW

CH. 7

Linear RegressionThe 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 WisdomSubsets 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 DataStraightening 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 RandomnessMaking and conducting simulations

Skill: Using random digits and using the calculator to help carry out simulations

SMW

CH. 11

Obtaining Good SamplesSimple 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 Studiesobservational studies vs. randomized comparative experiments; s; control treatments; blinding; placebos; blocking; factors; confounding variables vs. lurking variables

Basics of Experimental DesignSubjects, factors, treatments, explanatory & response variables, placebo effect, blinding; completely randomized design (CRD); diagrams

Principles of Experimental Designcontrol, 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 ConceptsProbability 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 RulesGeneral addition rule, Venn diagrams, union and intersection; general multiplication rule, definition of independence; conditional probability, tree diagrams; disjoint vs. independent SMW

CH. 15

Random VariablesDiscrete 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 VariablesBernoulli trials; probability density function (pdf) vs. cumulative density function (cdf)

Geometric Distributions – X = # of trials up to and including 1st 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 ModelsMoving 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 Proportionsconfidence 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 ProportionsSignificance 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 TestsDefinition 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 MeanDescribing 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 BlocksMatched pairs vs. two independent samples SMW

CH. 25

 

UNIT 7: INFERENCE WHEN VARIABLES ARE RELATED 12 DAYS
Chi-Square Goodness of Fit TestThe 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 RegressionPopulation 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

  1. Show Work – many answers in statistics are written in sentences and a one number answer value is usually not just the answer.

 

  1. 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

  1. Do the REVIEW
  2. Stay up, not catch up.  Turn Homework in on time!
  3. 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

  1. 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.