STATWAY INSTRUCTOR NOTES DAY ONE The objective of this lesson is to create a classroom community that will support and sustain students throughout the year-long course. It is also designed to introduce students to the norms and expectations around collaboration, discussion and support. DAY ONE Course Launch Productive Persistence Contract Activity ADDITIONAL MATERIALS As early as possible students should log on to the online platform MyStatway. The first time they do so, they will complete a background survey that will capture vital baseline information about student perception and knowledge. It s imperative that students complete this at the very beginning of the course. Once students have had the opportunity to complete assignments for a grade, you will want to complete the Syllabus Follow-Up Activity. MYSTATWAY Login Instructions 10 minutes PRODUCTIVE PERSISTENCE Syllabus Follow-Up Activity 20 minutes MODULE 1 The module begins with an introduction to the idea of statistical inference by having students conduct an in class experiment. In this vein students are guided through the research process, including developing a research question and deciding between an observational study and an experiment. The module concludes by exposing students to more detail about sampling methods and experimental design.
STATWAY INSTRUCTOR NOTES 2 has students conduct an in class experiment involving astrology. This sets the stage for a later formal development of inference by having students judge whether in class results are "unusual" relative to random variation. The topic then has students examine experiments and observational studies and the types of conclusions that can be drawn from each. LESSON 1.1.1 The Statistical Analysis Process Lesson 1.1.1 Supplement Astrology Investigation Lesson 1.1.1 Applet Match, Excel file Lesson 1.1.1 Productive Persistence Forming Groups Lesson 1.1.1 Productive Persistence Working in Groups 1 hour 40 minutes LESSON 1.1.1 EXTENSION Populations, Samples and Subjects and Mindset Activity Lesson 1.1.1 Extension Supplement 1 Growth Mindset Article Lesson 1.1.1 Extension Supplement 2 Mindset Questions LESSON 1.1.2 Samples, Populations, and Types of Statistical Studies 1 hour 40 minutes introduces students to sampling methods. The required lesson shows students the importance of randomness in sampling as well as the dangers of methods such as convenience sampling and voluntary response sampling. Two optional lessons introduce systematic sampling and stratified sampling and show student sources of bias in observational studies.
STATWAY INSTRUCTOR NOTES 3 LESSON 1.2.1 Random Sampling LESSON 1.2.2 Other Sampling Strategies Optional LESSON 1.2.3 Sources of Bias in Sampling Optional Lesson 1.2.3 Supplement A Survey Questions Lesson 1.2.3 Supplement B Survey Questions Topic 3 Topic 3 introduces students to experimental design. Students examine random assignment, direct control, control groups, and the placebo effect. An optional lesson shows how random assignment tends to create similar groups. LESSON 1.3.1 Collecting Data by Conducting an Experiment Lesson 1.3.1 Supplement The Gettysburg Address LESSON 1.3.2 Populations, Samples and Subjects Lesson 1.3.2 Supplement Dotplots 1 hour 40 minutes MODULE 2
STATWAY INSTRUCTOR NOTES 4 This module takes students into the third step of the research process, data analysis. The module starts with graphical summaries of data and then moves on to measures of center and spread. Module 2 also emphasizes the use of data analysis to compare distributions. focuses on how analyzing graphs can help with comparing distributions. Students compare dotplots and histograms and write summaries of the comparison between two distributions commenting on center, spread, and shape. LESSON 2.1.1 Dotplots, Histograms, and Distributions for Quantitative Data LESSON 2.1.1 Data Basketball Data, Excel file Lesson 1.2.3 Supplement B Survey Questions LESSON 2.1.2 Constructing Histograms for Quantitative Data LESSON 2.1.2 Supplement Histograms focuses on the most common measures of center, mean and median. The effects of outliers and skewing on each are examined to help students understand when each measure is most useful. LESSON 2.2.1 Quantifying the Center of a Distributiom Sample Mean and Sample Median Topic 3 Topic 3 introduces students to measures of dispersion based on the median. The students find the range, the quartiles, and the interquartile range. They draw boxplots as graphs of the fivenumber summaries and use the interquartile range to identify potential outliers.
STATWAY INSTRUCTOR NOTES 5 LESSON 2.3.1 Quantifying Variability Relative to the Median 1 hour 15 minutes Topic 4 Topic 4 introduces another measure of spread, standard deviation. Students examine deviations from the mean in order to derive the standard deviation and learn to interpret its meaning. LESSON 2.4.1 Quantifying Variability Relative to the Mean 1 hour 15 minutes MODULE 3 In this module, students transition from examining univariate numerical data to bivariate numerical data. Through exploration students learn to interpret and create scatterplots, as well as sketch lines (or curves) that best represent the data and use them to make predictions. Students use technology to create least squares regression lines and calculate correlation coefficients. They learn to interpret the parameters in the resulting model and understand the characteristics of the correlation coefficient and coefficient of determination. They use these along with the coefficient of determination, residual values, and residual plots to assess the fit of a line. In this topic students develop an understanding of the uses and value of scatterplots. They sketch lines of best fit and explore the role of the correlation coefficient in characterizing the strength and direction of linear relationships between explanatory and response variables. LESSON 3.1.1 Introduction to Scatterplots and Bivariate Relationships LESSON 3.1.1 Supplement Scatterplots 1 hour 30 minutes LESSON 3.1.2 Developing an Intuitive Sense of Form, Direction and Strength of the Relationship Between Two Measurements
STATWAY INSTRUCTOR NOTES 6 LESSON 3.1.3 Introduction to the Correlation Coefficient and Its Properties In this topic students develop an understanding of the minimization of squared error in the method of least squares. Students learn how to interpret the values of the parameters in the least squares line in context and when it is appropriate to use the regression line for prediction. LESSON 3.2.1 Using Lines to Make Prediction LESSON 3.2.2 Least Squares Regression Line as Line of Best Fit 1 hour 40 minutes LESSON 3.2.3 Investigating the Meaning of Numbers in the Equation of a Line LESSON 3.2.4 Special Properties of the Least Squares Regression Line Optional Topic 3 In this topic students examine residuals and how they can be used to assess the fit of a line. LESSON 3.3.1 Using Residuals to Determine If a Line is a Good Fit 1 hour 15 minutes LESSON 3.3.2 Using Residuals to Determine if a Line is an Appropriate Model Optional
STATWAY INSTRUCTOR NOTES 7 MODULE 4 Building upon Module 3 students will develop an understanding that other models, in addition to linear models, can be used to describe bivariate relationships. In particular, students will explore the exponential model. They will examine and learn to interpret the initial value parameter in context and whether a model represents a growth or decay scenario. Note: There is only one topic in this module. LESSON 4.1.1 Investigating Patterns in Data LESSON 4.1.2 Exponential Models MODULE 5 This module concentrates on categorical variables, and in particular relationship between pairs of categorical variables. Students use two-way tables and stacked bar graphs to examine such relationships. They calculate marginal, joint, and conditional proportions and probabilities. The module concludes by having students construct hypothetical two-way tables to calculate conditional probabilities. Note: There is only one topic in this module. LESSON 5.1.1 An Introduction to Two-Way Tables LESSON 5.1.1 Supplement Soda Data, Word file LESSON 5.1.1 Data Soda Data, Excel file LESSON 5.1.2
STATWAY INSTRUCTOR NOTES 8 Marginal, Joint, and Conditional Probabilities from Two-Way Tables LESSON 5.1.3 Building Two-Way Tables to Calculate Probability MODULE 6 This module develops the concepts of probability and probability distributions. Students explore The Law of Large Numbers and develop an understanding of basic probability rules by working with tables. The lessons also include both discrete and continuous probability distributions. In this topic students conduct an experiment that guides their understanding of The Law of Large Numbers. This is followed by an informal introduction to the basic probability rules using tables. Students also explore discrete random variables, discrete distributions and their properties. LESSON 6.1.1 Probability LESSON 6.1.2 Probability Rules LESSON 6.1.3 Simulation Optional LESSON 6.1.4 Probability Distributions of Discrete Random Variables In this topic continuous random variables are defined and explored. Students examine the normal distribution and the standard normal distribution.
STATWAY INSTRUCTOR NOTES 9 LESSON 6.2.1 Probability Distributions of Continuous Random Variables LESSON 6.2.2 Z-Scores and Normal Distributions Lesson 6.2.2 Supplement Empirical Rule LESSON 6.2.3 Using Normal Distributions to Find Probabilities and Critical Values MODULE 7 This module introduces sampling distributions and inferences for population proportions. Through simulations, distributions of sample proportions are discovered to have a familiar shape. With this discovery, students are introduced to the processes of statistical inference. Confidence intervals and hypothesis tests are informal, and determined through simulation. Through simulations, students investigate sampling distributions of sample proportions. After the ideas of shape, center and spread are explored, students use trial and error to determine margins of error that correspond to given levels of confidence. Students learn to create and properly interpret confidence intervals for a population proportion. LESSON 7.1.1 Sampling Distributions Lesson 7.1.1 Supplement Reese s Pieces Simulation, Excel File LESSON 7.1.2
STATWAY INSTRUCTOR NOTES 10 Reasoning with Sampling Distributions Lesson 7.1.2 Supplement Presidential Race Simulation, Excel file Lesson 7.1.2 Supplement Mayoral Race Simulation, Excel file LESSON 7.1.3 Confidence Intervals Lesson 7.1.3 Supplement Obama Approval Simulation, Excel file Lesson 7.1.3 Supplement Many Confidence Interval Simulation, Excel file introduces the logic and notation of hypothesis testing and the process for testing claims about a population proportion. Students use sampling distribution simulations to determine P- values that correspond to a particular observation. Proper conclusions and interpretations are discussed, along with the types of errors that can be made when conducting hypothesis tests. LESSON 7.2.1 Testing a Hypothesis Lesson 7.2.1 Supplement Euro Tossing Simulation, Excel file LESSON 7.2.2 Introduction to Hypothesis Testing MODULE 8 This module extends the ideas of Module 7 by demonstrating the approximate normality of the sampling distribution of sample proportions, thus leading to the Central Limit Theorem for sample proportions. Once
STATWAY INSTRUCTOR NOTES 11 criteria for approximate normality are established, students use the normal distribution to determine critical values for confidence intervals and P-values for hypothesis tests for a single population proportion. bridges the gap between simulated sampling distributions of sample proportions to the theoretical continuous and normal sampling distribution of sample proportions. Critical- and P- values from simulations and the normal distribution are compared, and criteria for approximate normality are presented. LESSON 8.1.1 The Central Limit Theorem for Sample Proportions Lesson 7.1.1 Supplement Population Proportion Simulation, Excel File LESSON 8.1.2 Finding Areas Under Sampling Distributions introduces confidence intervals for a population proportion. Margins of error are computed using normal distribution critical values, and students are led to understand how sample size and confidence level influence the margin of error. Emphasis is placed upon proper interpretation of confidence intervals. LESSON 8.2.1 Intervals for a Population Proportion and the Normal Distribution Lesson 8.2.1 Supplement Proportion and Interval Simulation, Excel file LESSON 8.2.2 Constructing Confidence Intervals for Population Proportions 20 minutes
STATWAY INSTRUCTOR NOTES 12 Topic 3 Topic 3 introduces hypothesis testing for a single population proportion. The normal distribution is used to determine P-values, which are used to make decisions regarding null and alternate hypotheses. Correct interpretation of results is emphasized. LESSON 8.3.1 Hypothesis Tests for Population Proportions LESSON 8.3.2 Additional Hypothesis Tests for Population Proportions MODULE 9 This module begins with an investigation of the sampling distribution of differences between sample proportions. Criteria for approximate normality are established, along with formulas for the mean and standard error. With these, students use the normal distribution to create confidence intervals and test hypotheses regarding differences between two population proportions. introduces the sampling distribution of differences between two sample proportions. Criteria for normality are introduced, and formulas for the mean and standard error of the sampling distribution are developed. LESSON 9.1.1 Sampling Distribution of Differences of Two Proportions LESSON 9.1.2 Using Technology to Explore the Sampling Distribution of the Differences in Two Proportions Lesson 9.1.2 Supplement Sampling Distribution Simulation, Excel file guides students in the construction of confidence intervals for differences between two population proportions. Margins of error are computed using the normal distribution and
STATWAY INSTRUCTOR NOTES 13 standard error, and the relationships between sample size, level of confidence, and margin of error are explored. Correct interpretation of confidence intervals for a difference between population proportions is stressed. LESSON 9.2.1 Confidence Intervals for the Difference in Two Population Proportions LESSON 9.2.2 Computing and Interpreting Confidence Intervals for the Difference in Two Population Proportions 30 minutes Topic 3 Topic 3 introduces hypothesis testing for the difference between two population proportions. Students learn to test hypotheses using P-values and make conclusions regarding the null and alternate hypotheses. Correct interpretation of results is emphasized. LESSON 9.3.1 A Statistical Test for the Difference in Two Population Proportions 30 minutes LESSON 9.3.2 Statistical Tests for the Difference Between Two Population Proportions MODULE 10 This module presents sampling distributions of sample means and the Central Limit Theorem for Sample Means. Sampling distributions of sample means are explored and used to construct confidence intervals for and perform hypothesis tests for population means. Paired data are used to make inferences on the population mean of differences, and data from independent samples are used to make inferences on the difference between two population means. In students explore sampling distributions of sample means from populations from a variety of distributions. Students use a simulation to determine that regardless of the
STATWAY INSTRUCTOR NOTES 14 population distribution, sampling distributions approach normality as the sample size increases. The lesson culminates with a presentation of the Central Limit Theorem for Sample Means. Students also explore how the mean and standard error of a sampling distribution relate to the mean and standard deviation of a population and to the sample size. LESSON 10.1.1 Sampling Distribution of Sample Means Lesson 10.1.1 Supplement Acorn Mass Table LESSON 10.1.2 Central Limit Theorem for Sample Means In students learn the rationale for using the T-distribution. They are introduced to critical values in T-distributions and construct confidence intervals based on sample data collected in class. LESSON 10.2.1 The T-Distribution and T-Statistics LESSON 10.2.2 Confidence Intervals for a Population Mean Topic 3 In Topic 3 students conduct formal hypothesis tests for population means. LESSON 10.3.1 Hypothesis Tests for Population Means Lesson 10.3.1 Supplement T-Table Topic 4 In Topic 4 students learn to how to differentiate between dependent and independent samples and construct confidence intervals and conduct hypothesis tests for the population mean of
STATWAY INSTRUCTOR NOTES 15 paired differences. They also learn to compute confidence intervals and conduct hypothesis tests for the difference between two population means. LESSON 10.4.1 Inferences from Paired Samples LESSON 10.4.2 Hypothesis Tests from Paired Samples LESSON 10.4.3 Inference from Independent Samples MODULE 11 This module presents categorical data analysis using the chi-square statistic. Students learn the processes of the chi-square goodness of fit test, the chi-square test for independence of two categorical variables and the chi-square test for homogeneity. In each case, students discover the logic behind the development of these tests, learn to conduct the tests and interpret their results in context. introduces the chi-square goodness of fit tests. Students are introduced to the chisquare test statistic, and learn the conditions under which it varies approximately according to the chi-square distribution. Test statistics and P-values are used to make conclusions regarding claims in goodness of fit tests. LESSON 11.1.1 Introduction to Chi-Squared Tests for One-Way Tables LESSON 11.1.2 Executing the Chi-Square Test for One-Way Tables (Goodness of Fit) LESSON 11.1.3
STATWAY INSTRUCTOR NOTES 16 The Chi-Square Distribution and Degrees of Freedom extends the use of the chi-square test statistic in tests for independence of categorical variables and homogeneity. LESSON 11.2.1 Introduction to Chi-Square for Two-Way Tables LESSON 11.2.2 Executing the Chi-Square Test for Independence in Two-Way Tables LESSON 11.2.3 The Chi-Square Test for Homogeneity in Two-Way Tables MODULE 12 This module presents a contrast between statistical models and deterministic, mathematical models. Students use algebra to develop an understanding of linear equations and find exact linear models given two points. Students learn to solve 1st degree equations and inequalities algebraically and graphically. This module includes optional lessons on solving quadratic inequalities and exponential functions. Students learn the difference between situations that require statistical methods for modeling versus the more exact (and in some ways, simpler) algebraic methods. Building upon the understanding of slope developed in Module 3, students learn to find the slope between two points and the equation of the line in form. LESSON 12.1.1 Statistical Models and Exact Mathematical Models of Linear Relationships 25 minutes LESSON 12.1.2 Mathematical Linear Models
STATWAY INSTRUCTOR NOTES 17 LESSON 12.1.3 Proportional Models Methods of solving 1st degree equations and inequalities are examined in this topic. Students learn how to solve equations and inequalities algebraically. They also learn how to solve inequalities graphically. LESSON 12.2.1 Linear Models Answering Various Types of Questions Algebraically LESSON 12.2.2 Solving Inequalities Topic 3 In this optional topic exponential and power models are explored. Students develop an understanding of the parameters of these models and are able to write equations given a description of a scenario. LESSON 12.3.1 Multiple Representations of Exponential Models Optional 1 hour 40 minutes LESSON 12.3.2 Power Models Optional +++++ STATWAY and the Carnegie Foundation logo are trademarks of the Carnegie Foundation for the Advancement of Teaching. A Pathway Through College Statistics may be used as provided in the CC BY license, but neither the Statway trademark nor the Carnegie Foundation logo may be used without the prior written consent of the Carnegie Foundation.
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