# Statistics

This is the Group for the Cohort 1 creating a course for Statistics.
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# Statistics Course Content

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Introductory statistics course developed through the Ohio Department of Higher Education OER Innovation Grant. The course is part of the Ohio Transfer Module and is also named TMM010. For more information about credit transfer between Ohio colleges and universities please visit: www.ohiohighered.org/transfer.Team LeadKameswarrao Casukhela                     Ohio State University – LimaContent ContributorsEmily Dennett                                       Central Ohio Technical CollegeSara Rollo                                            North Central State CollegeNicholas Shay                                      Central Ohio Technical CollegeChan Siriphokha                                   Clark State Community CollegeLibrarianJoy Gao                                                Ohio Wesleyan UniversityReview TeamAlice Taylor                                           University of Rio GrandeJim Cottrill                                             Ohio Dominican University

Material Type: Full Course

# Statistics Course Content, Continuous Random Variables – Uniform and Normal Distributions

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Material Type: Unit of Study

# Statistics Course Content, Continuous Random Variables – Uniform and Normal Distributions, Normal Distribution

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Many inferential procedures assume that variable(s) under study follow a normal distribution in the population. In this module we will study properties of this distribution and learn how to calculate important measures that would be useful later in inference.Learning Objectives:Understand the properties of a normal distribution, the graph of its density function, interpret areas enclosed by a normal curve over an interval, percentilesLearn and apply 68-95-99.7 Empirical RuleStandard normal distribution, z-scores and standard normal tableCompute areas under the normal curve and interpret the resultsCompute percentiles and interpret the resultsCalculate cut-off values of the variable to cover middle p% of the distributionHow normal is a population distribution - Learn how to infer that the population distribution of the variable is normal – set up hypothesis, use normal probability plot, Anderson-Darling normality test, interpret p-value of the testChapter 6 – Normal Distribution – Pages 361 - 375Suggested Exercises – Chapter 6 – Odds 60 through 80

Material Type: Module

# Introductory Statistics - Chapter 1: Sampling and Data

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Summary Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs. Senior Contributing Authors Barbara Illowsky, De Anza College Susan Dean, De Anza College

Material Type: Lesson, Module, Unit of Study

Author: Amanda Postle

# Introductory Statistics - Chapter 1: Sampling and Data, Key Terms

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1.1 Definitions of Statistics, Probability, and Key Terms The mathematical theory of statistics is easier to learn when you know the language. This module presents important terms that will be used throughout the text.

Material Type: Lesson, Module, Unit of Study

Author: Amanda Postle

# Statistics Course Content, Data Measurement and Types of Variables, Data, Measurement and Variables

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The study of a population, a process or a relationship of interest begins with collecting relevant data from representative samples. A good understanding of the key terms will help us design appropriate statistical analysis of the collected data.Learning Objectives:Distinguish between the terms – population, parameter, sample, statistics, and other key terms.Distinguish between different types of statistical studies – observational, experimental, retrospective or prospectiveLearn about different levels of measurement, data types, and variablesLearn about different ways of collecting data – Sampling Methods and ExperimentsIdentify sources of measurement bias and variabilityTextbook Material: Chapter 1, Sampling & DataSuggested Homework AssignmentChapter 1 – Pages 47 – 60 - Problems 42 to 62, 65, 67, 73, 74, 75, 78, 87, 91

Material Type: Module

# Statistics Course Content, Sampling Methods, Producing Data – Sampling Methods

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Producing Data – Sampling MethodsIn this module we will explore the different sampling methods to obtain representative samples from a population. We also learn about the relative advantages and disadvantages of each method. Learning Objectives:Reasons for samplingRandom Vs. Non-Random SamplesSampling Bias and VariabilityRandom Sampling Methods – Simple, Stratified, Systematic, Cluster and Multistage random samplesNon-Random Sampling Methods – Voluntary Response and Convenience samplingSample surveys, sampling errorsBest method of random samplingSampling distributions

Material Type: Module

# Statistics Course Content, Design of Experiments, Producting Data - Experimental Methods

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In this module we will study experimental designs. We will learn about the principles of a good experimental design, the relative advantages and disadvantages of each method.Learning Objectives:Principles of experimental designs – control, randomization and replicationExperimental Vs. Sampling MethodsComparative Experiments – Completely Randomized Design, Randomized Block Design, Factorial DesignMatched Pair DesignClinical Trial and Double-Blind ExperimentsExperimental Ethics

Material Type: Module

# Statistics Course Content, Graphical Descriptions of Data on a Single Variable, Graphical Presentation for Data on a Single Variable

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A data set is a listing of variables and their observed values on individuals or objects of study. In this topic we will learn about how to organize data on a single variable using frequency distributions which form the basis for constructing charts including Pie Charts, Bar Charts and Histograms. We also explore Stemplot. It is important to note that the type of chart to be used depends on the type of data/variable to be represented.Given a data set be able to construct a frequency table, find and interpret relative frequency of a value, find and interpret cumulative frequency.For categorical data make and interpret a Pie chart and a Bar Chart. Further know when to construct each type of chart, their relative advantages and limitations.For quantitative data be able to make and interpret Stemplot, Histogram, Frequency Polygon, Ogive, Time Series Graph. Further know when to construct each type of chart, their relative advantages and limitations. Textbook Material -  Chapter 1 – Sampling and Data – pages 13 – 19Chapter 2 – Descriptive Statistics – Pages 67 – 88

Material Type: Module

# Statistics Course Content, Numerical Descriptions of Data on Single Variable, Numerical Summary of Data

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A data set is a listing of variables and their observed values on individuals or objects of study. In this topic we will learn about numerical summaries of data on a single variable and learn how to use them to describe data distribution and determine unusual values in the data. The type of numerical summaries to use depend on the data. We will also learn about boxplots.Learning Objectives:Understand which numerical summaries must be used to represent dataBe able to compute and interpret them. Also, know their properties and relative advantages and disadvantages. Further, use these measures to describe distributions, compare values from distributions, detect unusual values in the data, etc.For categorical data use counts and proportions to describe categoriesFor quantitative data useMeasures of Center – Mean, Median, ModeMeasure of Spread – Range, Interquartile Range (IQR), Variance and Standard DeviationMeasures of Location – Minimum, Maximum, Quartiles and PercentilesLearn to distinguish between different types of distributions for quantitative data – symmetric, skewed, bell-shaped, multimodal distributionsLearn about Empirical Rule for bell-shaped distributionsUse z-scores to compare values and detect unusual valuesMake boxplot of dataTextbook Material: Chapter 2 – Descriptive Statistics – Pages 88 - 122Suggested HomeworkChapter 2 - Descriptive Statistics – 29, 31, 32, 43, 57, 60, 69, 71, 82, 84, 86, 88, 89, 104, 106, 108, 109, 115, 119

Material Type: Module

# Statistics Course Content, Probability Concepts, Introduction to Probability

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ProbabilityThe notion of chance or probability of an event plays a crucial role in statistics. In this module we will study this notion and learn different rules that will help us determine the probability of different types of events associated with a process.Learning Objectives:Random experiment, sample space, eventsPermutation and CombinationDefinition of probability of an event and its propertiesDisjoint and independent eventsConditional eventsVenn and Tree DiagramsComplement (Subtraction) ruleAddition ruleMultiplication ruleDivision ruleTwo-Way tablesTotal Probability Rule and Bayes Rule

Material Type: Module

# Statistics Course Content, Discrete Random Variables, Binomial Distribution, Discrete Random Variable, Binomial Distribution

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In this module we will learn about discrete random variables, their distributions and properties. Of specific interest would be a binomial random variable, its distribution and applications.Learning Objectives:Discrete random variable, distribution, mean and standard deviationBinomial random variable and its distributionTextbook Material -  Chapter 4 – Probability Topics – Pages 239 - 257Suggested Homework:Discrete Random Variable - 69, 70, 74, 75, 76, 78, 96, 102Binomial Distribution – Odds 88 - 111

Material Type: Module

# Statistics Course Content, Sampling Distributions of Sample Mean and Sample Proportion, Sampling Distributions and Central Limit Theorem

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Ideally a census will be able to provide answers to many questions about a population. However, a census is impractical in many ways. So we need to rely on information drawn from a carefully chosen random sample of individuals/objects from the population. Such information may include sample statistics - proportion, mean, median, standard deviation, correlation, distribution, etc. The downside of the sampling approach is that the information we get is bound to change when we take a different sample. Then how can we ensure that we can make reliable inference about the population using only the sample information we got from our sample? The answer lies in the sampling distribution of the statistic which allows us, under certain assumptions, to make predictions about its values. These predictions, in turn, can be compared with the actual values obtained in the sample.Learning Objectives:Sampling Distribution of the Sample MeanSampling Distribution of the Sample ProportionCentral Limit Theorem, its assumptions and conclusion. Textbook Material -  Chapter 7 – The Central Limit Theorem – Pages 395 – 401, 405 – 413Suggested Exercises – Chapter 7 – Odds 61 – 71, 76 – 93

Material Type: Module

# Statistics Course Content, Estimation of Single Population Mean and Single Population Proportion, Estimation of Population Mean and Population Proportion

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In this module we will explore the concept of a confidence interval to estimate an unknown population parameter. Specifically, we will obtain confidence interval estimates for unknown population mean and for unknown population proportion. We will also find how large a sample we would require to estimate these parameters for any given amount of accuracy and confidence level.Learning Objectives:Construct and interpret a confidence intervalStudent’s t-distributionStandard error and margin of errorSample size estimationTextbook Material -  Chapter 8 – Confidence Intervals – pages 439 - 463Suggested Exercises – Odds 97 – 134

Material Type: Module

# Statistics Course Content, Test of Significance - Inference for Population Mean and Population Proportion, Test of Hypothesis

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In this module we will explore tests of hypotheses about a population parameter. Specifically, we will learn about testing a claim about a population mean and a population proportion. Learning Objectives:Identify the parameter of the populationSpecify the null and alternative hypotheses for the parameterType I and Type II errorsLevel of significanceTest statistic and sampling distribution of a testP-value of a test and its interpretationCritical valueConclusion of a test, Statistical significanceTest of hypothesis for a population meanTest of hypothesis for a population proportionTextbook Material -  Chapter 9 – Hypothesis Testing with One Sample – pages 501 - 511

Material Type: Module

# Statistics Course Content, Correlation and Simple Linear Regression, Correlation and Simple Linear Regression

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Sometimes it is difficult to measure or find information on a variable of interest. The problem then is to use information from easily measurable variables to find the needed information. Naturally, the variables to use must be related to the variable of interest. In this module we will study about relationships between two quantitative variables. We will explore some standard mathematical (linear, quadratic, cubic, etc.) forms of relationships.Learning Objectives:Identify response and explanatory variablesGiven bivariate data make a scatterplot of data and predict the pattern and strength of the relationship between the variablesLinear relationshipDefine correlation, study its properties and use themFind correlation for a bivariate data and interpret the resultsInterpret the square of the correlationTest for the significance of correlation – set up hypothesis and interpret the p-value of the testLinear relationship – Estimate the linear relationship between the two variables.Interpret slope and intercept.Interpret the square of the correlationStudy residuals and residual plots,Distinguish between the terms correlation and causationTest for the significance of the slope coefficient – set up hypothesis and interpret the p-value of the test.Study quadratic and other non-linear models.Textbook Material -  Chapter 12 – Correlation and Regression – Pages 673 - 699

Material Type: Module