SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

 

 

Department:        Mathematics

Subject Area and Course Number:  Mathematics 117H

Course Title:   Elementary Statistics, Honors

Discipline:  Mathematics

Units:    4

Repeatability:    None

Catalog Course Description:  General education mathematics course.  Introduction to design of experiments, descriptive statistics and sampling distributions; the Central Limit Theorem, statistical inference, confidence interval estimation and tests of hypotheses; correlation and linear regression, categorical variables and Chi-square distribution, one-way ANOVA.

Description for Schedule of Classes:  Experimental design, data analysis, probability distributions, including binomial, normal, t. Sampling distributions, hypothesis testing, confidence intervals, correlation and regression, Chi-square and categorical variables, one-way ANOVA.

Lecture Hours per Week:    4.3  (64-72 Total Semester Hours)

Laboratory Hours per Week:          None

Plus Hours:            None

Prerequisites: Math 107 or Math 111, with grade of "C" or better or qualifying score on SBCC placement exam.

Co-requisites:  None

Skills Advisories:   Eligibility for English 110 or English 110H or English 110GB

Course Advisories:         None

Limitation on Enrollment:      Acceptance into Honors Program

Course Objectives:  By the end of the course, the student will be able to:

1.              Design a statistical experiment.

2.             Collect, organize, present, summarize, describe, analyze, and draw inferences from data.

3.             Read, analyze and write critiques of statistical studies.

4.             Use computer software statistics packages.

5.             Choose the correct statistical tools for decision making.

6.             Demonstrate the accurate use and understanding of statistical terminology.

7.             Write full paragraphs discussing the conclusions of a statistical test.

 

Course Content and Scope:  

A.        Introduction to Statistics.  Populations and parameters; samples and statistics.  Sampling and random numbers.

B.        Sampling and design of experiments.

C.        Descriptive Statistics

1.         Types of data:  nominal, ordinal, interval, ratio; discrete and continuous

2.         Summation notation

3.         Measures of central tendency:  mean, weighted mean, median, mode; calculation, properties, meaning and comparisons of them.

4.         Measures of position:  percentiles, deciles, quartiles, percentile rank.

5.         Variability:  range, variance, standard deviation, interquartile range.

6.         Frequency distributions:  Frequency, relative frequency and cumulative frequency tables and histograms; mean, variance and percentiles for grouped data.

7.         Relative measure of position:  z scores

D.        Probability Distributions

1.         Random variables:  discrete vs. continuous

2.         Discrete Probability distributions

a.         Mean, variance and standard deviation of discrete random variables and sum of discrete random variables

b.         Binomial Distribution:  Characterization of binomial experiments; binomial probability formula; mean, variance and standard deviation of the binomial.

3.         Continuous Probability Distributions

a.         Characteristics of continuous probability distributions and their graphs; the uniform distribution

b.         The general normal distribution and its characteristics; the empirical rule

c.         The standard normal distribution and z scores

d.         Normal tables, statistical calculators

e.         Normal approximation to the binomial

E.        The Central Limit Theorem and Sampling Distributions.

1.         The need for probability methods of sampling.

2.         Simple random sampling.

3.         Selecting a random sample.  Random number tables and generators.

4.         Other sampling methods.

5.         Sampling from finite populations

6.         The concept of a sampling distribution.

7.         The distribution of sample sums and sample means.

8.         The Central Limit Theorem and some of its applications.

F.         Estimation

1.         Point estimates.  Error of estimates. Confidence interval estimates

2.         Estimating the population mean with population variance known

3.         Estimating the population mean with population variance unknown

4.         Estimating the population variance and standard deviation

5.         Estimating population proportions

6.         Estimating differences in two population parameters:  means, proportions, variances

7.         Determination of sample size

G.        Hypothesis Testing

1.         Null and alternate hypotheses

2.         Decision errors:  Type I and II

3.         P values

4.         Tests concerning means for large samples

            a.         Single population

            b.         Two populations

5.         Tests concerning means for small samples

            a.         Single population

            b.         Two populations

6.         Tests of proportions

            a.         Single population

            b.         Two populations

H.        Correlation and Regression

1.         Scatter diagrams

2.         Correlation

            a.         The coefficient of linear correlation

            b.         Hypothesis tests concerning the population correlation coefficient

            c.         Confidence interval estimates of the population correlation coefficient

            d.         Misuses of correlation:  causation

3.         Linear regression

            a.         Least squares

            b.         Prediction intervals

            c.         The relationship between correlation and regression

I.          The Chi-Square Distribution

1.         Goodness of fit

2.         Contingency tables

J.         One-Way Analysis of Variance

1.         F-statistic distribution

2.         Multiple comparisons procedure

 

Methods of Instruction:  Learning by doing is integral to this course.  Traditional lecture supplemented with slides, films, projection of computer screens, and videotapes will be used to introduce topics.  Hands-on activities carried out in small groups will extend student understanding and skills.  Emphasis will be placed on applying lecture topics to related portions of the students' ongoing research projects.

 

Required Assignments: 

A.        Reading Assignments:  In addition to regular readings from the text, students will read supplemental articles.

B.        Writing Assignments:  Throughout the semester, students will submit written progress reports on their course research project, as well as written critiques of assigned articles. At the end of the semester, students will submit a written final report on their course research project.

C/D.   Appropriate Outside Assignments/Assignments that Demonstrate Critical Thinking:  Students will carry out a statistical research project which they will present to the class.  The research project will include, at a minimum, framing of hypotheses, designing and implementing a scheme for data collection, organizing and analyzing data (where feasible using statistical software), refining the hypotheses when indicated, drawing conclusions, and preparing a formal research report.  When possible, the research projects will be selected to coordinate with other courses in the Honors Program.

 

Methods of Evaluation:  Students' grades will be based on their performance on assigned written critiques, quizzes, examinations, the oral presentations and written reports of their research projects, and a comprehensive final examination.

 

Appropriate Texts and Supplies:

Larson, Farber, Elementary Statistics: Picturing the World, 4th Ed., Prentice Hall, 2007

Aliaga, Gunderson, Interactive Statistics, 3rd Ed., Prentice Hall, 2005

McLaughlin, Wakefield, Introduction to Data Analysis Using Minitab, 3rd Ed., Prentice Hall, 2005

TI-84 Graphing Calculator, Student Version of Minitab

Student Learning Outcomes:

1.                  Use statistical core terminology accurately.

2.                  Organize data using both numerical and graphical methods.

3.                  Use measures of central tendency and dispersion to summarize a data set.

4.                  Calculate probabilities of events explained by the normal and the standard normal distribution.

5.                  Estimate population parameters using confidence intervals.

6.                  Carry out a complete test of hypothesis about population parameters.

 

 

 

CO/mej

Revised August 2006; 8/24/09

FRC (Word Proc Center)