# High School Statistics Skills Practice

Skills available for High School Statistics Skills Practice
Introduction to Data Analysis
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Foundational Concepts
• Identifying Parameters
• How to Identify Statistics
• Identifying Individuals in a Data Set
Variables and Measurement
• How to Identify Variables in a Data Set
• How to Identify Quantitative Variables
• How to Identify Categorical Variables
• How to Classify Variables by Levels of Measurement
• How to Identify Discrete Variables
• How to Identify Continuous Variables
Categorical Data Analysis
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Analyzing One Categorical Variable
• How to Read a Pictograph
• How to Create a Pictograph
• Comparing Pictographs
• Interpreting Bar Charts
• How to Construct a Percent Bar Graph
• How to Compare Bar Charts
• Interpreting Double Bar Charts
• How to Create Double Bar Charts
• Comparing Double Bar Charts
• How to Read Circle Graphs
• How to Create a Pie Chart
• How to Compare Pie Charts
Analyzing Two Categorical Variables
• How to Interpret Venn Diagrams
• How to Create a Venn Diagram
• Interpreting Two-Way Frequency Tables
• Creating Two-Way Frequency Tables
• Interpreting Two-Way Relative Frequency Tables
• Creating Two-Way Relative Frequency Tables
• Comparing Two-Way Frequency Tables
• Creating Marginal Distributions
• How to Create a Conditional Distribution
• Computing Conditional Probability Using a 2-Way Frequency Table
• Computing Conditional Probability to Make an Inference Using a 2-Way Frequency Table
• Computing Conditional Probability Using a Large 2-Way Frequency Table Conditional Probability
Quantitative Data Analysis
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Analyzing One Quantitative Variable
• Interpreting Dot Plots
• How to Create Dot Plots
• Comparing Dot Plots
• Interpreting Line Plots
• Comparing Line Plots
• How to Interpret a Time Series Plots
• How to Create a Time Series Plot
• Comparing Time Series Plots
• How to Interpret a Histogram
• How to Create a Histogram
• How to Compare Two Histograms
• How to Interpret Stem-and-Leaf Plots
• Reading Data from Stem and Leaf Plots
• How to Interpret Back-to-Back Stem-and-Leaf Plots
• How to Create a Back-to-Back Stem-and-Leaf Plot
• How to Measure the Center of Data by Finding the Mean, Median, and Mode
• Comparing Mean, Median & Mode
• How to Calculate a Missing Data Value given the Mean of a Data Set
• How to Find Variance and Standard Deviation
• Calculating Population Standard Deviation
• How to Use Chebyshev's Theorem
• Summarizing a Data Set with a Five-Number Summary
• How to Find Interquartile Range
• Determining Whether to Use Mean & Standard Deviation or Median & IQR
• Determining Outliers Using Standard Deviation
• Determining Outliers Using the Fence Rule
• Interpreting Box-and-Whisker Plots
• Create a Box-and-Whisker Plot
• Comparing Box-and-Whisker Plots
• Interpreting Modified Box-and-Whisker Plots
• Creating Modified Box-and-Whisker Plots
• Comparing Modified Box-and-Whisker Plots
• How to Interpret Percentiles
• Interpreting Percentile Ranks
• How to Calculate Percentiles
• How to Calculate Quartiles
• How to Construct a Frequency Distribution
• How to Construct a Frequency Polygon
• Analyzing Cumulative Relative Frequency Graphs & Ogives
• How to Calculate Z-scores
• Calculating an Observed Value When Given a Z-Score & Distribution Parameters
• Comparing Z-scores
• Recalculating Summary Statistics Based on Linear Transformations
• Describing the Effects of Linear Transformations Using a Graph
• Labeling the Mean and Median of Density Curves Based on Shape
• Calculating Areas Under Density Curves
• Interpreting Areas Under Density Curves
• Describing Normal Distributions Using the Empirical Rule
• Using the Empirical Rule to Identify Values of a Normal Distribution
• Finding Probabilities under a Normal Curve Using the Empirical Rule
• Computing a Shaded Region's Standard Normal Probability When the Shaded Region is Less Than X
• Finding Probability Given a Basic Word Problem Involving Normal Distribution
• Finding Probability Given an Advanced Word Problem Involving Normal Distribution
• Computing a Shaded Region's Standard Normal Probability When the Shaded Region is Greater Than X
• Computing a Shaded Regions Standard Normal Probability When the Shaded Region is in Between X & Y
• Finding Thresholds for a Percentile
Analyzing Two Quantitative Variables
• How to Interpret a Scatterplot
• How to Create a Scatterplot
• How to Construct a Scatter Plot from a Table of Data on Given Axes with Integers
• Constructing a Scatter Plot from a Table of Data on Given Axes with Decimals
• Measuring the Strength of Linear Associations with a Correlation Coefficient
• Understanding Linear Relationship and the Correlation Coefficient
• Determining Outliers in a Scatterplot
• Determining the Least-Squares Regression Line Using Technology
• Interpreting the Slope of a Least-Squares Regression Line
• Interpreting the Y-intercept of a Least-Squares Regression Line
• Making Predictions Using the Least-Squares Regression Line
• How to Make Predictions from the Line of Best Fit
• How to Compute Residuals
• How to Interpret a Residual Plot
• Interpreting the Standard Deviation of the Residuals
• Interpreting Computer Output for Regressions
• Identifying the Effects of Removing Outliers on Regression Lines
• Classifying Linear and Nonlinear Relationships from Scatterplots
• Classifying Linear & Nonlinear Relationships from Scatter Plots
• Transforming Nonlinear Models to Linear
• Making Predictions Using Nonlinear Models
Study Design
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Observational Studies
• Writing Statistical Questions for Observational Studies
• Identifying the Population of Interest
• Differentiating Between Population of Interest & a Sample
• Identifying Bias in Sample Selection
• How to Select a Simple Random Sample
• Generating Random Samples From a Population with Known Characteristics
• Selecting a Cluster Random Sample
• How to Select a Systematic Random Sample
• How to Identify Bias in a Survey
• Analyzing Observational Studies
• Differentiating Between Correlation and Causation
• Identifying Correlation and Causation
• Conducting a Simulation Using a Table of Random Digits
Experimental Studies
• Identifying Outcomes in a Random Number Table Used to Simulate a Simple Event
• How to Use a Random Number Table to Simulate a Simple Event
• How to Generate a Random Number Table with Technology to Simulate a Simple Event
• Identifying Outcomes in a Random Number Table Used to Simulate a Compound Event
• How to use a Random Number Table to Simulate a Compound Event
• How to Design an Experimental Study
• Designing a Matched Pairs Experimental Study
• Identifying the Principles of Experimental Design Used in a Study
• Differentiating the Scopes of Inference for Studies
• Determining when an Experiment or Observational Study is Required
Probability
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Probability Basics
• Choosing an Appropriate Method for Gathering Data
• Choosing an Appropriate Basic Method For Gathering Data
• Determining a Sample Space For a Simple Event
• Determining Outcomes For a Simple Event
• Calculating Theoretical Probability
• Determining a Sample Space For a Compound Event
• Determining Outcomes for Complements of Events
• How to Shade a Venn Diagram to Indicate the Union of Events
• How to Shade a Venn Diagram to Indicate the Intersection of Events
• How to Shade a Venn Diagram to Indicate the Complement of an Event
• Calculating Probability Using a Venn Diagram
• How to Use the Addition Rule for Disjoint Events
• Solving a Word Problem Involving the Probability of a Union
• Calculating Event Probability Using the Addition Rule
• Solving a Word Problem Involving the Probability of an Intersection
• Computing the Conditional Probability of an Event
• Computing Conditional Probability Using a Sample Space
• Computing Basic Conditional Probability
• Using a Tree Diagram to Reverse the Condition
• Using Theoretical Probability Formulas to Determine Independence
Experimental Probability
• Identifying Independent & Dependent Events
• Using Probabilities to Identify Independent Events
• How to Calculate Experimental Probabilities
• Calculating Experimental Probability
Combinatorics
• Using a Tree Diagram to Count Outcomes
• Interpreting a Tree Diagram
• Introduction to Permutations
• Introduction to Combinations
• Solving Word Problems Involving Combinations
• Finding Probabilities Using Permutations
• How to Calculate Conditional Probabilities Using Combinations
Random Variables
• How to Identify a Random Variable in a Scenario
• Classifying Random Variables as Discrete or Continuous
• Constructing a Probability Distribution for a Discrete Random Variable
• How to Determine Valid Probability Distributions of Discrete Random Variables
• How to Calculate Probabilities Using Probability Distributions
• How to Calculate the Mean or Expected Value of a Discrete Random Variable
• How to Calculate the Variance of a Discrete Random Variable
• How to Calculate the Standard Deviation of a Discrete Random Variable
• Describing the Impact of Transformations on the Mean & Standard Deviation of a Random Variable
• How to Calculate the Mean or Expected Value of the Sum of Two Random Variables
• How to Calculate the Mean or Expected Value of the Difference of Two Random Variables
• How to Calculate the Variance of the Sum of Two Random Variables
• How to Calculate the Standard Deviation of the Sum of Two Random Variables
• How to Calculate the Variance of the Difference of Two Random Variables
• How to Calculate the Standard Deviation of the Difference of Two Random Variables
• Combining Normal Random Variables
• Recognizing Binomial Random Variables
• Approximating Independence with the 10 Percent Rule
• How to Interpret a Binomial Distribution
• How to Create a Binomial Distribution
• Finding the Probability of a Particular Number of Successes from a Binomial Probability Distribution
• Using the Binomial Formula to Solve a Basic Word Problem
• Using the Binomial Formula to Solve an Advanced Word Problem
• How to Calculate the Variance of a Binomial Distribution
• How to Calculate the Standard Deviation of a Binomial Distribution
• Recognizing Geometric Random Variables
• Finding the Probability for a Particular Value of a Geometric Random Variable
• Finding the Probability for a Range of Values of a Geometric Random Variable
• How to Calculate the Mean or Expected Value of a Geometric Distribution
• Calculating the Variance of a Geometric Distribution
• Calculating the Standard Deviation of a Geometric Distribution
• Recognizing Hypergeometric Random Variables
• Finding the Probability for a Particular Value of a Hypergeometric Random Variable
• Finding the Probability for a Range of Values of a Hypergeometric Random Variable
• How to Calculate the Mean or Expected Value of a Hypergeometric Distribution
• Calculating the Variance of a Hypergeometric Distribution
• Calculating the Standard Deviation of a Hypergeometric Distribution
• Recognizing Poisson Random Variables
• Finding the Probability for a Particular Value of a Poisson Random Variable
• Finding the Probability for a Range of Values of a Poisson Random Variable
• How to Calculate the Mean or Expected Value of a Poisson Distribution
• How to Calculate the Variance of a Poisson Distribution
• How to Calculate the Standard Deviation of a Poisson Distribution
• Recognizing a Continuous Uniform Distribution
• Finding the Probability for a Range of Values for a Continuous Uniform Distribution
• Calculating the Mean of a Continuous Uniform Distribution
• Calculating the Variance of a Continuous Uniform Distribution
• Calculating the Standard Deviation of a Continuous Uniform Distribution
Sampling Distributions
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Sampling Distribution of a Sample Proportion
• Determining the Mean of a Sampling Distribution of the Sample Proportion
• Calculating the Variance of the Sampling Distribution of a Sample Proportion
• Calculating the Standard Deviation of the Sampling Distribution of a Sample Proportion
Sampling Distribution of a Sample Mean
• Differentiating Between the Distribution of a Sample and the Sampling Distribution of Sample Means
• Applying the Central Limit Theorem to the Sampling Distribution of Sample Means
• Determining the Mean of the Sampling Distribution of a Sample Mean
• Calculating the Variance of the Sampling Distribution of a Sample Mean
• Calculating the Standard Deviation of the Sampling Distribution of a Sample Mean
• Calculating the Standard Error of the Sampling Distribution of a Sample Mean
• Determining Whether a Z-distribution or T-distribution is Appropriate
Confidence Intervals
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Introduction to Confidence Intervals
• How to Construct a Confidence Interval Given a Statistic & a Margin of Error
• How to Interpret a Confidence Interval
• How to Interpret a Confidence Level
Estimating a Population Proportion
• Verifying the Conditions for Creating a Confidence Interval for a Population Proportion
• How to Find the Critical Z-value for a Given Confidence Level
• Constructing a Confidence Interval for a Population Proportion
• Interpreting a Confidence Interval for a Population Proportion
• Determining a Sample Size for a Confidence Interval for a Population Proportion Based on Confidence & Margin of Error
Estimating a Population Mean
• Verifying the Conditions for Creating a Confidence Interval for a Population Mean
• Finding the Critical T-value for a Given Confidence Level & Sample Size
• How to Construct a Confidence Interval for a Population Mean
• How to Interpret a Confidence Interval for a Population Mean
• How to Construct a Confidence Interval for a Population Mean with Paired Data
• How to Interpret a Confidence Interval for a Population Mean with Paired Data
• Determining a Sample Size for a Confidence Interval for a Population Mean Based on Confidence & Margin of Error
• How to Construct a Confidence Interval With a Small Sample Size
Hypothesis Tests
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Significance Test Basics
• How to Write a Null Hypothesis For a Given Situation
• What is an Alternative Hypothesis For a Given Situation?
• Interpreting the Statistical Significance of Data Based on a P-Value & a Significance Level
• How to Interpret the Meaning of a Given P-Value
• How to Estimate a P-Value From a Simulation
• How to Make Valid Conclusions Using a P-Value
• Identifying a Type I Error of a Hypothesis Test
• Identifying a Consequence of a Type I Error of a Hypothesis Test
• Identifying a Type II Error of a Hypothesis Test
• Identifying a Consequence of a Type II Error of a Hypothesis Test
• Interpreting the Power of a Particular Significance Test
Hypothesis Test for Population Proportion
• Writing Hypotheses for a Significance Test for a Proportion
• Verifying the Conditions for Conducting a Hypothesis Test for a Proportion
• How to Calculate the Z-statistic for a Hypothesis Test for a Proportion
• Learn How to Determine a P-Value Given a Z-statistic for a Hypothesis Test for a Proportion from a Z-table
• How to Determine a P-Value Given a Z-statistic for a Hypothesis Test for a Proportion from Technology
• Making Valid Conclusions about a Hypothesis Test for a Proportion
Hypothesis Test for Population Mean
• Writing Hypotheses for a Significance Test for a Mean
• Verifying Conditions for Conducting a Hypothesis Test for a Mean are Met
• How to Calculate the T-statistic for a Hypothesis Test for a Mean
• How to Determine a P-Value Given a T-statistic for a Hypothesis Test for a Mean from a T-table
• How to Determine a P-Value Given a T-statistic for a Hypothesis Test for a Mean from Technology
• Making Valid Conclusions about a Hypothesis Test for a Mean
• How to Conduct a Sign Test
• How to Conduct a Wilcoxon Signed Rank Test
Two-Sample Inference
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Comparing Two Proportions
• How to Create a Confidence Interval for the Difference in Proportions of Two Independent Groups
• How to Interpret a Confidence Interval for the Difference in Proportions of Two Independent Groups
• How to Conduct a Hypothesis Test for the Difference in Proportions of Two Independent Groups
• How to Interpret the Results of a Hypothesis Test for the Difference in Proportions of Two Independent Groups
Comparing Two Means
• How to Create a Confidence Interval for the Difference in Means of Two Independent Groups
• How to Interpret a Confidence Interval for the Difference in Means of Two Independent Groups
• How to Conduct a Hypothesis Test for the Difference in Means of Two Independent Groups
• How to Interpret the Results of a Hypothesis Test for the Difference in Means of Two Independent Groups
Chi-square Tests
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Goodness-of-Fit Test
• Verifying the Conditions for Conducting a Chi-Square Goodness-of-Fit Test are Met
• How to Conduct a Chi-Square Goodness-of-Fit Test Using Technology
• How to Interpret a Chi-Square Goodness-of-Fit Test Using Technology
Test for Independence
• Verifying the Conditions for Conducting a Chi-Square Test for Independence are Met
• How to Conduct a Chi-Square Test for Independence Using Technology
• How to Interpret a Chi-Square Test for Independence Using Technology
Test for Homogeneity
• Verifying the Conditions for Conducting a Chi-Square Test for Homogeneity are Met
• How to Conduct a Chi-Square Test for Homogeneity Using Technology
• How to Interpret a Chi-Square Test for Homogeneity Using Technology
Linear Regression Inference
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Confidence Interval for Slope
• Verifying the Conditions for Creating a Confidence Interval for a Slope of a Regression Line are Met
• How to Create a Confidence Interval for the Slope of a Regression Line
• How to Interpret a Confidence Interval for the Slope of a Regression Line
• Using a Confidence Interval to Test the Slope
Hypothesis Test for Slope
• Verifying the Conditions for a Hypothesis Test for Linearity
• How to Write Hypotheses for a Hypothesis Test for the Slope of a Regression Line
• How to Calculate a T-Statistic for the Slope of Regression Line
• How to Determine the P-Value for a Hypothesis Test for Linearity Using Technology
Analysis of Variance (ANOVA)
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ANOVA Tests
• How to Calculate the Total Sum of Squares (SST)
• How to Calculate the Total Sum of Squares Within and Between (SSW and SSB)
• Verifying the Conditions for Conducting an ANOVA F-Test are Met
• How to Conduct an ANOVA F-Test Using Technology
• How to Interpret the Results of an ANOVA F-Test Using Technology
• How to Interpret Group Means from a Factorial Design
• How to Interpret Control Charts

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