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Course Proposals (Drafts)

Course Outlines

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Math 15 --- Elementary Statistics

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Catalog Description

The study of statistical methods as applied to descriptive statistics and inferential statistics. An emphasis on the meaning and use of statistical significance will be central to the course. Students will use frequency distributions, graphs, measures of relative standing, measures of central tendency, measures of variability, correlation, and linear regression to explore descriptive statistics. Students will use the laws of probability and statistical tests (t-tests, chi-square, ANOVA, and regression analysis) to make decisions via hypothesis testing and estimate parameters using confidence intervals.

Special notes or advisories: A TI-83 or TI-84 graphing calculator is required.

Prerequisites

Math 120 (or equivalent) with a grade of "C" or better or appropriate score on the math placement exam.

Describe representative skills without which the student would be highly unlikely to succeed: Intermediate algebra provides the mathematical content level needed to succeed in this course, as well as the ability to persist when the critical thinking involved becomes more advanced. Particular skills include the use of set-notation and logic, inequalities, square roots, function notation, linear functions, and percents. Ability to solve algebraic equations analytically, graphically, numerically and verbally in real-world settings. Ability to use technology in the study of these functions.

Recommended Preparation

English 150 (or equivalent)

Rationale for Recommended Preparation: Students will benefit from a higher level of reading competency at this level of mathematics. In addition, the written assignments are better suited for students that have at least this level of writing skills.

Course Learning Outcomes

What should the student be able to do as a result of taking this course? State some of the objectives in terms of specific, measurable student accomplishments.

1. Accurately communicate statistical ideas using correct statistical notation, graphs, and vocabulary.
2. Use descriptive and inferential statistics to solve real-world problems.
3. Demonstrate appropriate use of technology in making decisions based upon real-world data.
4. Demonstrate the characteristics of an effective learner and critical thinker, such as note-taking, critical reading, communication through writing, verbal discussions, the ability to work as part of a group, etc.
5. Read and interpret information that contains statistical analysis and be able to communicate these results.
6. Judge the validity of research reported in the mass media and peer reviewed journals.

Course Content

• Themes: What themes, if any, are threaded throughout the learning experiences in this course?
  • The importance of statistics in the decision-making process.
  • The use of statistics in the real world.
  • Critical thinking.
  • Problem solving.
  • Writing.
  • Technology.
  • Communication.
• 
  
• Concepts: What concepts do students need to understand to demonstrate course outcomes?
  • The statistical decision-making process.
  • The presentation of statistical methods in a logical, coherent structure, including the use of writing skills, grammar, and punctuation.
  • The use of technology as a statistical problem-solving tool.
  • Interpreting graphs.
  • p-value.
  • Type I and Type II error.
  • The connection between the p-value, test statistic, and statistical significance.
  • The recognition that reporting statistical results requires good communication skills.
• 
  
• Issues: What primary issues or problems, if any, must students understand to achieve course outcomes.
  • The appropriate use of technology in the problem-solving process.
  • The connection between statistics, science, and the real world.
  • The role of the student in becoming a successful learner.
  • The recognition that the problem-solving skills learned in this class are applicable in future mathematics classes, classes in related fields, as well as in the real world.
  • The importance of writing mathematics using correct notation and grammar.
  • Reading unfamiliar mathematics using their text and other resources.
• 
  
• Skills: What skills must students master to demonstrate course outcomes?
  1. Fundamentals of Statistical Analysis
  • State the appropriate null and alternative hypotheses, and determine the direction of extreme.
  • Interpret Type I and Type II errors for given hypotheses.
  • Validate assumptions of the hypothesis test.
  • Form a decision rule based on the level of significance.
  • Calculate the appropriate test statistic.
  • Compute the p-value and use it to decide which hypothesis is supported.
  • Create an interval estimate of a parameter.
  2. Data Studies and Sampling
  • Gather data using probability sampling methods.
  • Recognize different types of sampling bias.
  • State the difference between observational versus experimental studies.
  • Recognize bias in articles from the mass media and professional journals.
  3. Summarizing Data
  • Distinguish between different types of data variables.
  • Create appropriate displays of distributions (bar graphs, pie charts, frequency tables, stem-and-leaf plots, frequency plots, boxplots, histograms, scatterplots).
  • Identify shapes of distributions.
  • Calculate the appropriate measure of center (mean, median, mode) for a given set of data.
  • Calculate the appropriate measure of spread (range, interquartile range, standard deviation) for a given set of data.
  • Calculate measures of relative standing.
  • Calculate a linear transformation and standardize data.
  4. Modeling Distributions
  • Model a population with the appropriate distribution of a random variable.
  • Calculate the proportion associated with a given range of values from a random variable.
  • Calculate the range of values of a random variable associated with a given proportion.
  5. Probability
  • Calculate probabilities through simulations using technology.
  • List a sample space and identify events of interest in the sample space.
  • Calculate probabilities using the rules of probability.
  6. Sampling Distributions
  • Calculate the sampling distribution of the sample proportion.
  • Calculate the sampling distribution of a sample mean.
  7. Testing Hypotheses and Confidence Intervals For Proportions and Means
  • Demonstrate the connection between confidence intervals and hypothesis testing.
  • Identify the appropriate conditions for using hypothesis tests for population proportions or population means.
  • Create a confidence interval estimate for a population proportion or a population mean.
  • Conduct a hypothesis test and create a confidence interval estimate for two population proportions.
  • Conduct hypotheses tests and create confidence interval estimates for means of paired and independent samples.
  8. One-Way Analysis of Variance
  • Validate the assumptions in one-way ANOVA.
  • Determine the corresponding F-distribution.
  • Perform a one-way ANOVA test.
  9. Relationships Between Two Quantitative Variables
  • Display the relationship and determine if a linear model is appropriate.
  • Calculate the least squares regression model.
  • Perform residual analysis and identify influential points and outliers.
  • Determine if the linear relationship is statistically significant.
  • Calculate r, the correlation coefficient.
  • Recognize the relationship between r and the slope.
  • Interpret the coefficient of determination r^2.
  10. The Chi-Square Statistic
  • Perform a test of the goodness of fit.
  • Perform tests of homogeneity and of independence.

Representative Learning Activities

What will the students be doing (i.e., Listening to lectures, participating in discussions and/or group activities, attending a field trip, etc.)? Relate the activities directly to the Course Learning Outcomes.

• Listening to lectures.
• Participating in group activities and/or assignments.
• Participating in class assignments and/or discussions.
• Completing homework assignments.
• Reading mass media and/or journal articles that contain statistical analyses.
• Completing online activities on the computer.
• Using the graphing technology to complete activities designed to foster a deeper level of understanding of the concepts and skills developed in this class.

Assessment Tasks

How will the student show evidence of achieving the Course Learning Outcomes? Indicate which assessments (if any) are required for all sections.

• Representative assessment tasks:
• • In-class examinations and/or quizzes.
  • Homework assignments.
  • Take-home examinations and/or quizzes.
  • Writing assignments to develop communication of statistical concepts.
  • Group projects and other in-class activities.
  • Portfolios and/or reference books.
  • Group and/or individual projects and presentations.
• Required assessments for all sections – to include but not limited to:
• • Collaborative and individual homework assignments.
  • Examinations and/or quizzes.

Examples of Appropriate Texts or Other Readings

• Author: Martha Aliaga/Brenda Johnson; Title: Interactive Statistics, Third Edition; Date: 2006
• Author: David Salsburg; Title: The Lady Tasting TEa: How Statistics Revolutionized Science in the Twentieth Century; Date: 2001
• Author: David Lane; Title: http://onlinestatbook.com/index.html(online section); Date: 2007