## Active Outline

Credit- Degree applicable | ||

Effective Quarter: Fall 2020 | ||

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## MATH 10 | ## Introductory Statistics | ## 5 Unit(s) |

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**II. Course Objectives**

A. | Explore statistical techniques and process statistical information in order to make decisions about the reliability of a statement, claim or "fact"; Identify the standard methods of obtaining data and identify advantages and disadvantages of each. |

B. | Examine the nature of uncertainty and randomness and set up data collection methods that are free of bias; Distinguish among different scales of measurement and their implications. |

C. | Organize, display, summarize, and interpret data using graphical and statistical techniques; Interpret data displayed in tables and graphically; Calculate measures of central tendency and variation for a given data set. |

D. | Use probability to model and understand randomness; Apply concepts of sample space and probability. |

E. | Examine distributions of data using graphical and analytical methods; Calculate the mean and variance of a discrete distribution. |

F. | Describe data distribution through the study of sampling distributions; Distinguish the difference between sample and population distributions and analyze the role played by the Central Limit Theorem. |

G. | Estimate parameters by constructing point estimates and confidence intervals; Calculate probabilities using normal and t-distributions; Construct and interpret confidence intervals. |

H. | Compose probability statements about how confident one can be about making decisions based on data and construct the Type I and Type II error probabilities based on this decision; Determine and interpret levels of statistical significance including p-values; Interpret the output of a technology-based statistical analysis; Identify the basic concept of hypothesis testing including Type I and II errors; Formulate hypothesis tests involving samples from one and two populations; Select the appropriate technique for testing a hypothesis and interpret the result. |

I. | Compose conjectures about bivariate and ANOVA theoretical models; Use linear regression analysis and ANOVA for estimation and inference, and interpret the associated statistics. |

J. | Use appropriate statistical techniques to analyze and interpret applications based on data from disciplines including business, social sciences, psychology, life sciences, health sciences and education. |

**III. Essential Student Materials**

Graphing calculator (at discretion of instructor) |

**IV. Essential College Facilities**

Computer lab |

**V. Expanded Description: Content and Form**

A. | Explore statistical techniques and process statistical information in order to make decisions about the reliability of a statement, claim or "fact"; Identify the standard methods of obtaining data and identify advantages and disadvantages of each. |

1. | Recognize that statistics is an applied branch of mathematics and a unique discipline. |

2. | Use proper statistical techniques for gathering data |

3. | Access published statistical information in a variety of formats |

4. | Understand how statistics uses mathematical logic to measure uncertainty |

5. | Understand the major components of statistics: descriptive and inferential |

6. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

B. | Examine the nature of uncertainty and randomness and set up data collection methods that are free of bias; Distinguish among different scales of measurement and their implications. |

1. | The origins of randomness in antiquity (see http://faculty.deanza.fhda.edu/mathiosdiane/) and its difference from deterministic models |

2. | The need to model uncertainty |

3. | Data and sampling methods |

4. | Distinguish among different scales of measurement and their implications |

5. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

C. | Organize, display, summarize, and interpret data using graphical and statistical techniques; Interpret data displayed in tables and graphically; Calculate measures of central tendency and variation for a given data set. |

1. | Graphical techniques for data: stem leaf, histogram, box plots |

2. | Descriptions of the shape of data: symmetrical or skewed |

3. | Descriptions of the center of data: mean, median, mode |

4. | Descriptions of variation of the data: range, variance, standard deviation |

5. | Descriptions of the location of data: quartile, percentile, z score, interquartile range |

6. | Identify outliers |

7. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

D. | Use probability to model and understand randomness; Apply concepts of sample space and probability. |

1. | The historical origins of probability theory in 17th century Europe (optional) |

2. | Modeling random outcomes |

a. | Sample spaces |

b. | Events |

c. | Tree diagrams and (optional) Venn diagrams |

d. | Compound events: the use of "and" and "or" (multiplication and addition rules) |

e. | Complements |

3. | Independent and mutually exclusive events |

4. | Conditional probabilities |

5. | Bayes' Theorem (optional) |

6. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

E. | Examine distributions of data using graphical and analytical methods; Calculate the mean and variance of a discrete distribution. |

1. | Discrete Probability Distributions |

a. | Discrete random variables: expected value and variance |

b. | Binomial distribution |

1. | Properties of the Binomial Distribution |

2. | The origins of the Binomial Distribution in the arithmetic triangle of China and Pascal and the historical development of binomial probabilities by the Bernoulli family (optional) |

c. | Conceptual understanding of other discrete probability distributions (optional): |

1. | Poisson Distribution |

2. | Hypergeometric Distribution |

3. | Geometric distribution |

4. | Negative Binomial (Pascal) Distribution |

2. | Continuous Probability Distributions |

a. | Continuous random variables: probability is equal to area |

b. | Area (probability) and percentile computations |

c. | Normal (Gaussian) Distribution |

1. | The normal random variable |

2. | Standard normal distribution |

3. | Its historical development by Carl Friedrich Gauss in the 19th century (optional) |

4. | The normal approximation to the binomial (optional) |

d. | Additional continuous probability distributions (optional) |

1. | Uniform distribution |

2. | Exponential distribution |

3. | Linear distribution |

3. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

F. | Describe data distribution through the study of sampling distributions; Distinguish the difference between sample and population distributions and analyze the role played by the Central Limit Theorem. |

1. | Creating patterns through simulation |

2. | The Central Limit Theorem for averages and (optional) sums |

3. | The historical origins of the Central Limit Theorem in the early 19th century (optional) |

4. | The Law of Large Numbers (optional) |

5. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

G. | Estimate parameters by constructing point estimates and confidence intervals; Calculate probabilities using normal and t-distributions; Construct and interpret confidence intervals. |

1. | Point estimation |

2. | Confidence intervals for population means (population standard deviation known) |

3. | The Student t distribution |

a. | The historical origins of the Student-t distribution by William Gosset in the early 20th century, including its use in small sample sizes (optional) |

b. | Population standard deviation not known |

c. | General assumptions about the Student-t distribution |

4. | Confidence intervals for population means (population standard deviation unknown) |

5. | Confidence intervals for population proportions |

6. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

H. | Compose probability statements about how confident one can be about making decisions based on data and construct the Type I and Type II error probabilities based on this decision; Determine and interpret levels of statistical significance including p-values; Interpret the output of a technology-based statistical analysis; Identify the basic concept of hypothesis testing including Type I and II errors; Formulate hypothesis tests involving samples from one and two populations; Select the appropriate technique for testing a hypothesis and interpret the result. |

1. | The nature of hypothesis testing; Z-tests and t-tests for one population. |

a. | Formulating the null and alternative hypotheses |

b. | The p-value approach |

c. | The decision approach given a fixed significance |

d. | The four decisions |

1. | The Type I error probability |

2. | The Type II error/Power probability concept (calculations are optional) |

3. | Determining when statistical significance really matters |

2. | The Chi Square Distribution |

a. | Developing and checking distributional assumptions |

b. | Major uses |

c. | Contingency Tables: independence and homogeneity |

d. | At least one of the following: |

1. | Goodness of Fit |

2. | Single variance |

3. | Testing Multiple Population Parameters |

a. | Two sample means: matched pairs and independent groups |

b. | At least one of the following: |

1. | Two proportions |

2. | Two variances and the F distribution |

4. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

I. | Compose conjectures about bivariate and ANOVA theoretical models; Use linear regression analysis and ANOVA for estimation and inference, and interpret the associated statistics. |

1. | Scatterplots |

2. | Correlation |

3. | Outliers and influential points |

4. | Least squares regression |

a. | Historical origins of the least squares method in the early 19th century (optional) |

b. | Overview of method of least squares |

5. | Prediction |

a. | Meaning and interpretation |

b. | Confidence intervals (optional) |

c. | Inference (optional) |

6. | Checking assumptions |

7. | The One Way Analysis of Variance (ANOVA) |

a. | Multiple means |

b. | Checking assumptions |

8. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

J. | Use appropriate statistical techniques to analyze and interpret applications based on data from disciplines including business, social sciences, psychology, life sciences, health sciences and education. |

1. | Typical examples may include |

a. | Decisions and Risk |

1. | Shipping and quality control decisions based on probabilities |

2. | Testing claimed percent of rape victims |

3. | Testing claimed percent of female suicide victims |

4. | Comparison of percents of various ethnic groups at community colleges |

5. | Comparison of percents of various ethnic groups in foster care |

6. | Comparing return on investment (ROI) on investment portfolios: maximizing expected returns, minimizing variance and volatility |

7. | Analyzing overbooking in airline reservations |

8. | Determining guarantee periods and analyzing the effect of changes in guarantee periods |

9. | Determining which location of a firehouse to close |

b. | Games of Chance |

1. | Modeling games such as Vietnamese "Lucky Dice" using discrete distributions |

2. | Using simulation as a tool to understand probabilities and analyze strategy in games such as the "Monte Hall" Problem |

c. | Estimation and Inference |

1. | Distribution of AIDS cases in Santa Clara county by ethnicity |

2. | Distribution of percentages of ethnic groups in San Francisco compared to observed percents |

3. | Collecting data to use hypothesis testing to challenge established beliefs |

4. | Analyzing medical treatments to compare effectiveness or safety of treatment vs placebo, or comparing more than one treatment |

5. | Analyzing the effectiveness of welfare or other social programs |

d. | Descriptive Statistics: |

1. | Heights and weights of male and female athletes |

2. | AIDS factors and drug use comparisons for males and females |

3. | Comparisons of percentage of persons below the poverty level for males and females |

4. | Racial profiling (test of independence) |

5. | Ethnic and gender distribution of De Anza students |

6. | Language spoken at home by Santa Clara County, CA and the U. S. |

7. | Discrimination in mortgage lending (DASL) |

8. | Literacy rates by gender, nation, and/or ethnicity |

9. | Percent of people who smoke by educational status |

10. | Demographic statistics such as life expectancy, teenage birth rates, poverty rates, attained educational level, unemployment, income, etc, internationally, nationally, or regionally, by gender, age, ethnicity, or geographic region |

2. | Use statistical knowledge to recognize and discuss provocative inferences and conclusions reported by the media, especially in regards to controversial current events issues, e.g. presidential and political elections, educational reform and trends, nutritional claims, and census sampling vs. counting |

3. | Recognize some contemporary contributors to the field of statistics (optional - see web site http://faculty.deanza.fhda.edu/mathiosdiane/ for references) |

4. | Statistical analysis using technology such as SPSS, EXCEL, Minitab, or graphing calculators. |

**VI. Assignments**

A. | Required readings from the text and other (optional) sources |

B. | Problem solving exercises that include written explanations of concepts and justification of conclusions. These exercises may be based upon real data. |

C. | Technology based projects/activities that include written descriptions of methods and results, and justification of conclusions. These technology based projects/activities may be based upon real, simulated or collected data. |

D. | Collaborative activities requiring conversation in small groups. |

E. | Two hour comprehensive final examination composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format. |

**VII. Methods of Instruction**

Lecture and visual aids Discussion of assigned reading Discussion and problem solving performed in class In-class exploration of Internet sites Quiz and examination review performed in class Homework and extended projects Guest speakers Collaborative learning and small group exercises Collaborative projects Activities which involve students in formal exercises of data collection and analysis Problem solving and exploration activities using applications software Problem solving and exploration activities using courseware |

**VIII. Methods of Evaluating Objectives**

A. | A minimum of two one hour examinations composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format. |

B. | A minimum of three technology based projects/activities that make use of graphing calculators or computers addressing randomness, variation, and simulation will be evaluated for accuracy, completeness, and proper use of techniques and methods discussed in class. Questions may also require the student to communicate ideas and conclusions in short essay format. For examples, see applicable activities in the Scheaffer book listed in Supporting References. |

C. | Two-hour comprehensive final examination composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format. |

D. | Problem-solving exercises (homework) and/or quizzes will be evaluated for accuracy and completion in order to assess student’s comprehension of the material covered in lecture and to provide feedback to students on their progress. Questions may also require the student to communicate ideas and conclusions orally or in short essay format. |

E. | Classroom participation and interaction in the discussion of the subject matter in small groups. This may include discussion of real-world statistics applications addressing contemporary social issues. |

**IX. Texts and Supporting References**

A. | Examples of Primary Texts and References |

1. | OpenStax College, Introductory Statistics, openstaxcollege.org, 2013. |

2. | Brase/Brase,"Understandable Statistics: Concepts and Methods", 12th Ed., Brooks Cole, Cengage Learning Systems, 2018. |

3. | Geraghty, Maurice. "Inferential Statistics and Probability - A Holistic Approach", Licensed under a Creative Commons-Attribution-ShareAlike 4.0, 2018. |

4. | Navidi and Monk, "Elementary Statistics", 2nd Ed., McGraw Hill, 2015. |

5. | Soler, Frank. Statistics. "Understanding Uncertainty". 4th ed. Associated Research Consultants, Cupertino 2017. |

B. | Examples of Supporting Texts and References |

1. | Bluman, "Elementary Statistics, A Step by Step Approach, A Brief Version" 6th ed. McGraw Hill 2013. |

2. | Devore, Jay L. "Probability and Statistics for Engineering and the Sciences". 9th ed. Cengage 2016. |

3. | Larson and Farber. "Elementary Statistics Picturing the World". 6th ed. Pearson 2014. |

4. | Packel, Edward. "The Mathematics of Games and Gambling" 2nd ed. The Mathematical Association of America, 2006. |

5. | Peck, R., et al. “Statistics: A .Guide to the Unknown” 4th ed. Cengage 2006. |

6. | Scheaffer, Richard L. "Activity Based Statistics" 2nd ed. Wiley eBook 2009. |

7. | Stigler,Stephen M. "The History of Statistics, The Measurement of Uncertainty before 1900". Belknap Press, 1990. |

8. | Sullivan III, Michael. “Statistics: Informed Decisions Using Data”. 5th ed. Pearson 2017. |

9. | Tintle, Rossman, Chance, et al. "Introduction to Statistical Investigations", 16th ed, Wiley, 2018. |

10. | Triola, Mario F. "Elementary Statistics", 13th edition, Pearson, 2017. |

11. | http://nebula2.deanza.edu/~stats - De Anza College Math 10 Curriculum - Supporting Internet references |