SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

 

Department:        Mathematics

Subject Area and Course Number:  Mathematics 117

Course Title:   Elementary Statistics

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 analysis of variance and multiple comparisons procedure.

Description for Schedule of Classes:  General education mathematics course.  Experimental design, descriptive statistics and sampling distributions; confidence intervals, hypothesis testing, correlation, linear regression, Chi-square and one-way analysis of variance.

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:      None

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

1.              Demonstrate the ability to use statistical terminology accurately.

2.             Produce and interpret statistical software outputs with standard statistical computations and analyses.

3.             Demonstrate mastery of techniques in descriptive statistics:

a.       Collect, organize and present data in standard ways, like pie charts, histograms and diagrams.

b.       Interpret information provided in standard ways, like pie charts, histograms and diagrams.

c.       Interpret information summarized by measures of central tendency.

d.       Interpret information summarized by measures of position, like quartiles and percentiles.

4.             Recognize and implement an experimental design.

5.             Distinguish between discrete and continuous random variables.

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

7.             Demonstrate mastery of techniques in inferential statistics.

a.       Estimate single population means and single population proportions with confidence intervals.

b.       Estimate the difference of two means and two proportions with confidence intervals.

c.       Determine the margin of error when using point estimates.

d.       Determine the sample size necessary to obtain a predetermined margin of error when estimating with confidence intervals.

e.       Test hypotheses about a single population mean and a single population proportion.

f.         Test hypotheses about the difference of two population means and two population proportions.

g.       Test hypotheses about the difference among several population means (one-way ANOVA).

h.       Apply and interpret multiple comparisons procedure.

8.             Demonstrate mastery of concepts in correlation and regression.

a.       Compute and interpret the value of the correlation coefficient between two continuous variables.

b.       Compute and interpret the line of best fit for two continuous variables.

c.       Use the line of best fit to determine predicted values of a continuous variable.

d.       Analyze common misuses of linear regression and correlation.

e.       Distinguish between correlation and causation.

9.             Analyze the assumed distribution of one categorical variable using the chi square distribution.

10.          Analyze the association of two categorical variables using the chi square distribution.

11.          Read, analyze and write critiques of statistical studies as reported by the media.

12.          Produce and interpret statistical software (typically MINITAB) outputs.

13.          Write conclusions derived from a statistical study using statistical terminology.

 

Course Content and Scope:  

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

B.        Introduction to sampling and design of experiments.

C.        Descriptive Statistics

1.         Types of data:  discrete and continuous

2.         Measures of position:  quartiles, percentiles

3.         Measures of central tendency:  mean, median.  Calculation and properties

4.         Measures of variability:  range, variance, standard deviation, interquartile range

5.         Frequency distributions:  relative and cumulative frequency tables, histograms

6.         Relative measures of position for data from normally distributed populations:  z scores

D.        Sampling Distributions and Probability

1.         Random variables:  discrete vs. continuous

2.         Discrete probability distributions

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

b.         Binomial distribution:  binomial experiments, binomial probability formula; mean, variance and standard deviations of the binomial

3.         Continuous probability distributions

a.         Characteristics of continuous probability distributions, graphs

b.         The general and standard normal distributions

E.        Estimation

1.         Point estimates.  Error. Confidence interval estimates

2.         Estimating the population mean with population variance known or unknown

3.         Estimating the population proportion

4.         Estimating differences in two population parameters:  means, proportions

5.         Determination of sample size

F.         Hypothesis Testing

1.         Null and alternate hypotheses

2.         P-values

3.         Tests for means using large samples:  one population, two populations

4.         Tests for means using small samples:  one population, two populations, t-tests

5.         Tests for proportions:  one population, two populations

6.         Tests for several means:  F-tests.

G.        Correlation and Linear Regression

1.         Scatter diagrams

2.         Correlation.  The coefficient of linear correlation. Misuses of correlation. Causation

3.         Linear Regression

a.         Line of least squares.  Predicted values using the line of least squares

b.         Misuses of linear regression.  Extrapolation

H.        Categorical Variables

1.         Goodness of fit

2.         Contingency tables

I.          One-way Analysis of Variance

1.         F-test for testing the hypotheses of differences among several means

2.         Multiple comparisons procedure

 

Methods of Instruction:  Learning by doing is the focus of this course.  Formal lecture is combined with the use of slides, films and projection of computer screens.  Assignments in the computer lab and learning center are integral components of the course.  Some classes use multimedia CD-ROMs to supplement lectures.

 

A hybrid Online version of the course is offered.

 

Required Assignments: 

A.        Reading Assignments:  will be assigned from the text and from mainstream publications.

B.        Writing Assignments:  submissions of writing samples analyzing and describing conclusions of a statistical test.

C.        Appropriate Outside Assignments:  videotapes in the learning center.

D.        Use of statistical software (MINITAB) is available in the computer lab.

E.        Appropriate Assignments that Demonstrate Critical Thinking:  students will analyze and critique the methodologies and conclusions of popular media articles or professional journal articles.

 

Methods of Evaluation:  The grade for the course will be based on multiple measures of performance in the interpretation and solution of statistical problems.  These measures include three one-hour exams and a comprehensive final examination requiring demonstration of problem solving skills.  In addition, instructors make use of quizzes, written homework, computer lab assignments and a statistical research project to judge a student's mastery of the subject and familiarity with statistical terminology and procedures.

 

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)