# MAT 12O ELEMENTARY STATISTICS I

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1 LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 12O ELEMENTARY STATISTICS I 3 Lecture Hours, 1 Lab Hour, 3 Credits Pre-Requisite: MAT 096 or Waiver Catalog Description: This course serves as a study of fundamental concepts and computational techniques of elementary statistics. Among the topics studied are: measures of central tendency, standard deviation, percentiles, statistical graphs, binomial and normal distributions, probability, correlation, regression, confidence intervals, and hypothesis testing. A statistical software package will be used to obtain basic sample statistics, to simulate fundamental theorems, study correlation and regression, and to assist with hypothesis testing. Purposes and Goals: Upon the completion of this course, students should be able to: 1. Perform basic statistical analyses of real-life data sets. They should be able to use standard statistical software on these data. 2. Transfer to four-year colleges and universities and pursue upper division courses and academic programs. 3. Review statistical analyses that involve the statistical procedures and methods presented in this course. 4. Communicate statistical ideas and analyses to audiences who may have little or no knowledge of statistics. Course Syllabus 1

2 Instructional Objectives: The instructor is expected to: 1. Explain the nature of statistics to the students, illustrate the key role statistics has in the technical aspect of life as well as its everyday applicability, and introduce the basic ideas and concerns about the processes used to obtain sample data. 2. Present how data sets can be organized or summarized through the use of tables, graphical displays, and descriptive measures. 3. Introduce the basic concepts of probability and the rules that apply to the probability of both simple and compound events. 4. Introduce the binomial, normal, and Student s t distributions and explain how they can be applied to estimate population parameters and conduct hypothesis tests. Instructor should clarify the assumptions and limitations of the statistical techniques that are based on these distributions. 5. Introduce the concepts of correlation and regression, explain how to use them to study bivariate data, and discuss how to use the regression equation to make predictions. 6. Explain how to use a statistical computer software package to organize, summarize, and analyze data sets in applied settings. 7. Guide students in reviewing statistical articles and in communicating statistical ideas and analyses. Performance Objectives: As a result of successful completion of this course, students should be able to: 1. Classify statistical studies as either descriptive or inferential. 2. Distinguish between populations and samples in an inferential study, compare different sampling methods, and describe possible sample biases. 3. Classify variables as either qualitative or quantitative, and discrete or continuous. 4. Create and interpret frequency distributions and graphs representing data sets. Course Syllabus 2

3 5. Obtain and interpret descriptive measures of univariate data sets for both samples and populations. Be able to distinguish between a parameter and a statistic. 6. Recognize and apply the basic definitions and rules of probability theory. 7. Examine binomial, normal, and Student s t random variables and their probability distributions. Be able to analyze a data set and determine which probability distribution is the best model to fit the data set. 8. Determine the sampling distribution of the mean for either a normally distributed variable or a variable that is not normally distributed, and state and apply the central limit theorem. 9. Use the normal or the Student s t-distribution to estimate population parameters and conduct hypothesis tests. 10. Utilize a statistical computer software package to organize and summarize information clearly and effectively, determine and compare descriptive measures of data sets, and use them to analyze data sets. 11. Utilize a statistical computer software package to simulate experiments in probability, simulate the sampling distribution of the mean, and illustrate the central limit theorem. 12. Use a statistical computer software package to obtain a one-sample t-confidence interval and perform a one-sample t-test for a population mean. 13. Use a statistical computer software package to obtain linear regression equation and compute linear correlation coefficient for bivariate data. 14. Read and interpret the results of linear correlation and regression presented in the output obtained from a statistical computer software package. Attendance/Lateness Policy Students are expected to attend all class meetings. Students are responsible for all information, material, and assignments covered in class regardless of class attendance. As per college policy, students who have more than 8 hours of unexcused absences don t meet the attendance requirement for passing the course. Students who miss more than 50% of the class period might Course Syllabus 3

5 Course Content Outline The timeline below is a suggestion and the course pacing may be adjusted by your instructor. Symbol refers to the SPSS technology tutorial videos linked to the Tools for Success tab of the toolbar menu on MyStatLab homepage. Additional technology resources will be posted on the MEC website and indicated by your instructor as needed. HOUR TOPIC SECTION PAGE MyStatLab Data Collection (Chapter 1) 1 2 Introduction to Practice of Statistics Section 1.1 HW Section 1.3 HW Population, Sample, Individual, Types of Variables, Parameter vs. Statistic 1.3, Section 1.4 HW Section 1.5 HW Sampling Methods Chapter 1 Review Quiz Sources of Bias Chapter 1 Review HW 3 Summarizing Data in Tables and Graphs (Chapter 2) Organizing Qualitative data Section 2.1 HW Frequency Distribution, Relative Frequency Distribution, Bar Graphs, Pareto Chart, Comparing Two Data Sets, Pie Charts LAB 1 Introduction to SPSS Opening /creating/editing SPSS data file Introduction to SPSS Data Manipulation: Sorting and Sampling (optional) Sampling (optional) 5 Organizing Quantitative Data Section 2.2 HW Frequency Distributions and Histogram for discrete and continuous data, Stem-and-leaf Plot, Dot Plot, Shape of a distribution Graphical Misrepresentation of Data Section 2.4 HW Chapter 2 Review Quiz Chapter 2 Review HW 6 Numerically Summarizing Data (Chapter 3) Measures of Central Tendency (raw data) Section 3.1 HW Mean, Median, Mode, using mean, median and mode to identify the shape of a distribution Course Syllabus 5

6 7 Measures of Dispersion (raw data) LAB 2 Basic Concepts, Range, Standard Deviation and Variance for sample and population, Comparing Variation, Interpreting Standard Deviation, Empirical Rule Using SPSS to organize and Summarize Data: Obtain frequency distributions, graphs and charts and descriptive statistics 9 Measures of Central Tendency and Dispersion (grouped data) Mean of a variable from grouped data, Weighted Mean Section 3.2 HW Descriptive Statistics, Histogram and Boxplot, Assessing Normality etc Section 3.3 HW 10 Measures of Position and Outliers Section 3.4 HW Z-score, Quartiles and Percentiles, Outliers 11 The Five-Number Summary and Boxplots Section 3.5 HW Chapter 3 Review Quiz Chapter 3 Review HW LAB 3 More SPSS Graphs and Charts: Stemand-Leaf Plot, Quartiles, Box-Plot, comparing data Descriptive Statistics, Histogram and Boxplot, Assessing Normality etc. 13 Review for Instructors Test #1 (Chapters 1, 2 and3) 14 Instructors Test #1 15 Describing the Relation between Two Variables (Chapter 4) Scatter Diagram and Correlation: Section 4.1 HW Scatter plot: draw and interpret, Pearson s Linear Correlation Coefficient: Meaning and Properties Regression Line /Equation: Section 4.2 HW Interpret Coefficients, Use for Prediction Contingency Tables and Association (optional) Section 4.4 HW Chapter 4 Review Quiz Chapter 4 Review HW Course Syllabus 6

7 LAB 4 Use SPSS to make a Scatter-plot with a Regression Line, produce and understand Linear Correlation and Regression Output 17 Probability and Probability Distributions: (Chapter 5) Probability Rules Empirical and Classical methods The Addition Rule & Complements Independence and the Multiplication Rule Conditional Probability and the General Multiplication Rule LAB 5 Use SPSS to Simulate Randomness Simulating Data based on Probabilities 21 Discrete Probability Distributions (Chapter 6) Discrete Random Variables A Discrete Probability Distribution Table, Probability Histogram Compute mean of Discrete Random Variable Interpret the mean as Expected Value Scatter-plot Regression and Residual Plots Correlation Section 5.1 HW Section 5.2 HW Section 5.3 HW Section 5.4 HW Chapter 5 Review Quiz Chapter 5 Review HW. Sampling (if not covered in Lab 1) Generating Random Numbers Section 6.1 HW Binomial Probability Distributions Criteria for a binomial probability experiment, Computing Binomial Probability: Table and Formula LAB 6 Simulate Binomial Random Variable, obtain Table of Binomial Probabilities, compute descriptive measures from a Probability Distributions Section 6.2 HW Course Syllabus 7

8 25 Binomial Probability Distributions Mean, Variance, and Standard Deviation of a Binomial Random Variable, Histogram, Check for Unusual Results 26 The Normal Probability Distributions (Chapter 7) Properties of the Normal Distribution Graph and Properties of the Normal Curve Area as Probability 27 Applications of the Normal LAB 7 Distributions The Standard Normal Distribution Using z-table: Finding Probabilities Given z Scores, Finding z Scores for given Areas Generate and study shape of Binomial Distribution bar graph, as the value of p changes 29 Applications of the Normal Distributions Finding Probabilities for given Values, Finding Values corresponding to Probabilities 30 Review for Test #2 31 Test #2 LAB 8 Simulating normal random variable, finding Probabilities for given scores, finding scores for given probabilities, Determining Normality (Q-Q Plot) 33 Sampling Distributions (Chapter 8) Distribution of the Sample Mean Sampling distribution, Mean and Standard Deviation of the Sampling Distribution, The Central Limit Theorem , Chapter 6 Review Quiz Chapter 6 Review HW Section 7.1 HW Section 7.2 HW Section 7.2 HW 393 Chapter 7 Review Quiz Chapter 7 Review HW Finding Inverse Normality (Finding z-scores Given an Area) and the Area under the Normal Curve Section 8.1 HW Chapter 8 Review Quiz Chapter 8 Review HW Course Syllabus 8

9 34 Estimating the Value of a Parameter (Chapter 9) Estimating a Population Mean Point Estimates, Confidence Intervals and their Interpretations, Meaning of Margin of Error, Constructing CI with σ known, Determining Sample Size Required 35 Estimating a Population Mean Properties of Student s t-distribution Finding t-values LAB 9 Use SPSS to explore Sampling Distribution of the mean for cases where population is Normal, and cases where population is not Normal. Access normality using Q-Q plots. 37 Estimating a Population Mean (σ Unknown) Construct and Interpret a Confidence Interval using Student s t-distribution Hypothesis Test Regarding a Parameter (Chapter 10) The Language of Hypothesis Testing Null and Alternate Hypothesis, Type I and Type II errors, Conclusions to Hypothesis Tests LAB 10 Estimating a Population Mean with SPSS using Confidence Intervals Hypothesis Testing about Population Mean, Hypothesis Tests for a Population Mean Traditional & P-value Methods ( σ unknown) σ -known case is optional Significance: statistical vs. practical LAB 11 Review for Test #3 45 Test # Final Examination Review Section 9.2 HW Descriptive Statistics,,Assessing Normality and Generating Confidence Intervals Section 9.2 HW Chapter 9 Review Quiz Chapter 9 Review HW Section 10.1 HW Hypothesis test for One Sample Mean and Associated Confidence Intervals Section 10.3 HW Chapter 10 Review Quiz Chapter 10 ReviewHW Course Syllabus 9

10 Data Analysis Projects and Activities Instructors will assign and evaluate at least 3 mini-projects or one course-long master project. Students should prepare a project report for each project assigned. The report must include the method(s) used for the data analysis and the interpretations of the numerical results. Some suggested projects from the course package are listed below. Use of SPSS or other professional software package is recommended for data analysis projects. Topic Chapter Page Exercise # Understanding Data Collection 1 62 Making an Informed Decision: What college should I attend (1-3) Organizing Qualitative Data Organizing Quantitative Data Consumer Reports: Consumer Reports Rates Treadmills Chap. 2: Case study (The Day the Sky Roared) Measure of Central Tendency Measure of Dispersion Five number Summary and Box-plot Consumer Reports: Basement Waterproofing Making an Informed Decision: What car should I buy Scatter Diagram and Correlation Least Square Regression Consumer Reports: Fit to Drink (a d) Making an Informed Decision:relationship between variables on the World scale Probability Chap. 5: Case study (The Case of the Body in the Bag) The Binomial Probability Distribution Making an Informed Decision: Should we convict? Applications of Normal Distribution Consumer Reports: Sunscreens Chap. 7: Case study (The Tale of Blood Chemistry and Health) Estimating The Value of a Parameter Consumer Reports: Consumer Reports Tests Tires Hypothesis Testing Chap. 10: Case study (How old is Stonehenge) A sample course-long master project (Data Analyses Project: Historical temperature Trends) is available on MEC website at bb Course Grading: HW Assignments, Quizzes 10% Data Analyses Projects and Activities 15% 3 Instructor Exams 45% Departmental Final Examination 30% Course Syllabus 10

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