Foothill CollegeApproved Course Outlines

Physical Sciences, Mathematics & Engineering Division
MATH 10ELEMENTARY STATISTICSFall 2012
5 hours lecture.5 Units

Total Quarter Learning Hours: 60 (Total of All Lecture, Lecture/Lab, and Lab hours X 12)
 
 Lecture Hours: 5 Lab Hours: Lecture/Lab:
 Note: If Lab hours are specified, see item 10. Lab Content below.

Repeatability -
Statement: Not Repeatable.

Status -
 Course Status: ActiveGrading: Letter Grade with P/NP option
 Degree Status: ApplicableCredit Status: Credit
 Degree or Certificate Requirement: AA Degree,   Foothill GE
 GE Status: Communication & Analytical Thinking

Articulation Office Information -
 Transferability: BothValidation: 07/01/2009; 11/22/11

1. Description -
An introduction to modern methods of descriptive statistics, including collection and presentation of data; measures of central tendency and dispersion; probability; sampling distributions; hypothesis testing and statistical inference; linear regression and correlation; analysis of variance; use of microcomputers for statistical calculations. Illustrations taken from the fields of business, economics, medicine, engineering, education, psychology, sociology and from culturally diverse situations.
Prerequisite: Satisfactory score on the mathematics placement test or MATH 105 or 108.
Co-requisite: None
Advisory: Demonstrated proficiency in English by placement into ENGL 1A as determined by score on the English placement test or through an equivalent placement process; UC will grant transfer credit for a maximum of one course from the following: PSYC 7, SOC 7 or MATH 10.

2. Course Objectives -
The student will be able to:
  1. distinguish between quantitative and qualitative data; sample and population; descriptive statistics and inferential statistics.
  2. read a graph and conclude what information the graph is conveying about the data.
  3. calculate measures of central tendency, dispersion and relative standing and use these measures to solve application problems.
  4. compute basic probabilities.
  5. define discrete probability distributions and use such distributions to solve application problems.
  6. define continuous probability distributions and use such distributions to solve application problems.
  7. define sampling distributions, state the Central Limit Theorem and use sampling distributions and the Central Limit Theorem to solve application problems.
  8. use confidence intervals to estimate population parameters, or the difference between two population parameters, using the appropriate formula and then interpret the result.
  9. determine the sample size required to estimate a population parameter.
  10. design, set up, and evaluate the results of hypothesis tests.
  11. compare and contrast the use of confidence intervals and hypothesis tests to make inferences about population parameters.
  12. solve application problems utilizing techniques of regression and correlation.
  13. use analysis of variance to make inferences about more than two population means.
  14. solve application problems using categorical data analysis.
  15. demonstrate statistical understanding of inference by participating in a cooperative project.
  16. demonstrate proficiency in the use of the computer as a tool for doing statistics
  17. apply statistical methods to situations in a culturally diverse society.
  18. discuss mathematical problems and write solutions in accurate mathematical language and notation.
  19. interpret mathematical solutions.
3. Special Facilities and/or Equipment -
  1. Graphing calculator
  2. Access to Microsoft Excel software
  3. When taught on Foothill Global Access: ongoing access to a computer with e-mail software and e-mail address.

4. Course Content (Body of knowledge) -
  1. Organization of Data
    1. Definitions
      1. population
      2. sample
      3. variables
      4. descriptive statistics
      5. inferential statistics
    2. Sampling Methods
      1. simple random
      2. stratified
      3. cluster
      4. systematic
      5. convenience
    3. Frequency and relative frequency distributions
  2. Graphs and charts
    1. histograms
    2. pie-charts
    3. stem-and-leaf graphs
    4. bar charts
    5. Pareto charts
    6. box plots
    7. dot plots
    8. ogives
    9. time-series
    10. graph shapes
  3. Measures of Central Tendency and Dispersion
    1. Summation notion
    2. Measures of central tendency
      1. mean
      2. median
      3. mode
    3. Measures of dispersion
      1. range
      2. sample variance
      3. sample standard deviation
      4. coefficient of variation
    4. Chebyshev's Theorem
    5. Percentiles and Quartiles
  4. Probability
    1. Empirical probability
    2. Sample spaces and events
      1. addition rule
      2. mutually exclusive events
      3. complementary events
    3. Conditional probability
      1. independent events
      2. multiplication rule
  5. Discrete Probability Distributions
    1. Definition of random variables
    2. Discrete random variables
      1. mean
      2. variance
      3. standard deviation
    3. Properties of a probability distribution function
    4. The Binomial distribution
      1. the binomial probability distribution function
      2. mean
      3. variance
      4. standard deviation
      5. application problems
  6. Continuous Probability Distributions
    1. Continuous random variables; equating area under a curve with probability
    2. Empirical Rule
    3. The normal distribution
      1. standardizing normal curves (z-scores)
      2. finding z-scores from areas under the standard normal curve
      3. application problems
    4. The normal approximation to the binomial distribution
      1. requirements
      2. adjusting the interval of the variable from discrete to continuous
  7. Sampling Distributions
    1. Sampling distribution of the mean
      1. mean
      2. standard deviation
      3. shape
      4. Central Limit Theorem
  8. Estimation
    1. Margin of Error
    2. Point estimation; biased and unbiased estimator
    3. Confidence interval for the mean when the variance is known
      1. maximal margin of error
      2. sample size for estimating the mean
    4. Confidence interval for the mean when the population variance is unknown
      1. maximal margin of error
      2. students t-distribution
      3. degrees of freedom
    5. Confidence interval for the population proportion
      1. maximal margin of error
      2. sample size for estimating the proportion
    6. Confidence interval for the difference between two means when population variances are known
      1. maximal margin of error
    7. Confidence interval for the difference between two means when population variances are unknown, but assumed unequal
      1. maximal margin of error
    8. Confidence interval for the difference between two means when population variances are unknown, but assumed equal
      1. maximal margin of error
    9. Confidence interval for the difference between two means when the samples are dependent
    10. Confidence interval for the difference between population proportions
      1. maximal margin of error
  9. Hypothesis Testing
    1. Vocabulary
      1. null hypothesis
      2. alternate hypothesis
      3. right-, left-, and two-tailed tests
    2. Mechanics of hypothesis testing
      1. type I error
      2. type II error
      3. p-value
      4. test statistic
      5. decision rule
      6. rejection and acceptance region
    3. Single-population hypothesis testing
      1. for the population mean when the variance is known
      2. for the population mean when the variance is unknown
      3. testing population proportion
    4. Two-population hypothesis testing
      1. comparing two population means when the population variances are known
      2. comparing two population means when the population variances are unknown, but assumed equal
      3. comparing two population means when the population variances are unknown, but assumed unequal
      4. dependent samples
      5. testing difference in population proportions
  10. Comparision of Hypothesis Tests and Confidence Intervals
    1. connection between hypothesis testing and confidence intervals
    2. statistical significance in confidence intervals and hypothesis tests
  11. Linear Regression and Linear Correlation
    1. Linear relations
    2. Linear regression
      1. scatter diagrams
      2. method of least squares
      3. regression analysis
      4. coefficient of determination
    3. Linear correlation
  12. One Way Analysis of Variance (ANOVA)
    1. Methodology
    2. F-distribution
    3. Tukey pairwise comparisons
  13. Chi Square Tests
    1. Contingency tables
    2. Chi-square distribution
    3. Tests for dependence of categorical variables
    4. Tests for homogeneity
    5. Goodness of fit
  14. Testing and Estimating a Population Variance
    1. Testing the variance
    2. Confidence intervals
  15. Cooperative Project
    1. Hypothesis testing
    2. Confidence intervals
    3. Graphs
    4. Statistical inference
    5. Sampling methods
    6. Data analysis
  16. Computer as a Tool for Doing Statistics
    1. Computer lab assignments
    2. Excel
  17. Examples used will be from different societies and cultures
  18. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
    1. Application problems from other disciplines
    2. Proper notation
  19. Interpret mathematical solutions.
    1. Explain the significance of solutions to application problems.
5. Repeatability - Moved to header area.
 
6. Methods of Evaluation -
  1. Homework
  2. Quizzes, mid-term exams
  3. Computer lab assignments
  4. Cooperative project
  5. Proctored comprehensive final examination: the final exam must be taken in person at the Los Altos Hills campus or at another approved facility administered by a proctor deemed acceptable by the instructor.
7. Representative Text(s) -
Beoga.net Inc. Elementary Statistics. V2.5. 2006.
Brase, H. and C. Brase. Understandable Statistics: Concepts and Methods, 9th ed. Houghton Mifflin, 2009.
When taught on Foothill Global Access: lectures, handouts, and assignments are delivered via e-mail and/or the world wide web.

8. Disciplines -
Mathematics
 
9. Method of Instruction -
Lecture, Discussion, Cooperative learning exercises, Lecture-Laboratory.
 
10. Lab Content -
Not applicable.
 
11. Honors Description - No longer used. Integrated into main description section.
 
12. Types and/or Examples of Required Reading, Writing and Outside of Class Assignments -
  1. Homework Problems: Homework problems covering subject matter from text and related material ranging from 30 - 60 problems per week.
Students will need to employ critical thinking in order to complete assignments.
  • Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
  • Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of Excel.
  • Worksheets: Problems and activities covering the subject matter.
  • Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.
    13. Need/Justification -
    This course is a required core course for the AS degree in General Studies Science and satisfies the Foothill GE Requirement for Area V, Communication & Analytical Thinking.


    Course status: Active
    Last updated: 2014-04-03 15:54:00


    Foothill CollegeApproved Course Outlines