Get Stronger: Practice Pages

Additional practice problems that help develop a deeper understanding of the concepts in the Learn It and Apply It.

Module 1

• Data Collection and Organization
• Statistical Questions
• Random Sampling
• Sampling Methods

Module 2

• Experimental Design
• Observational Studies
• Advanced Experimental Design
• Complex Graphical Displays
• Effective Visualizations

Module 3

• Displaying Categorical Data
• Applications of Bar Graphs
• Visualizing Quantitative Data
• Distribution of Quantitative Variables
• Comparing Quantitative Distributions

Module 4

• Measures of Center
• Interpreting the Mean and Median
• Boxplot Data and Displays
• Measures of Variability
• Z-Score and the Empirical Rule

Module 5

Module 6

• Probability
  
• Probabilities of Two Events
  
• Conditional Probabilities

Module 7

• Probability Distributions
• Normal Distribution
• Normal Distribution (continued)

Module 8

• Inference Basics
• Sampling Distribution of a Sample Proportion
• Sampling Variability

Module 9

• Confidence Interval for Proportions
• Confidence Interval for Proportions (continued)
• Sample Size for Proportions
• Confidence Intervals for the Difference in Population Proportions

Module 10

• Null and Alternative Hypotheses
• Test Statistics
• P-Value
• One-Sample Hypothesis Test for Proportions
• Errors in Hypothesis Testing
• Two-Sample Test for Proportions
• Connecting Tests and Intervals

Module 11

• Sampling Distribution of a Sample Mean
• t-distribution
• Confidence Interval for Population Mean
• Confidence Interval for Difference in Population Means

Module 12

Null and Alternative Hypothesis for Means
One-Sample Hypothesis Test for Means
Comparing Two Population Means (Independent Samples)
Comparing Two Population Means (Dependent Samples)

Module 13

Introduction to One-Way ANOVA
Conditions for ANOVA
ANOVA
Pair-wise Comparisons for ANOVA

Module 14

Introduction to Chi-Square Statistics
Chi-Square Test for Goodness of Fit 
Chi-Square Test of Homogeneity
Chi-Square Test of Independence
Fisher’s Exact Test

Module 15

Test for Significance of Slope
ANOVA for Regression
Confidence Interval and Prediction Interval
Transforming Data

Module 16

Multiple Linear Regression
Indicator Variable
Interaction Terms

Module 17

Bootstrap Distribution and Confidence Interval for a Population Mean
Bootstrap Confidence Interval
Simulation-Based Hypothesis Test for a Population Proportion
Simulation-Based Hypothesis Test for a Difference in Proportions

Module 18

Module 19

Discrete Probability Distributions
Binomial Distribution
Connection Between Binomial and Normal Distributions

Additional Practice:

• More Conditional Probabilities

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Statistical Technology Tools

These tools are linked throughout the course so you can solve problems and visualize data in different ways. You can access each tool directly via the links below.

Tool Name	Description
Anova (One-Way)	Obtain the ANOVA table, F-statistic and side-by-side boxplots to check assumptions. Carry out pairwise comparisons, including simultaneous confidence intervals for pairwise differences of means.
Association Between Two Categorical Variables	Construct 2 x 2 contingency tables, obtain conditional proportions, and get a bar graph. Find the difference or ratio of proportions to describe the strength of the association. Build the sampling distribution of the difference or ratio via resampling.
Compare Two Population Means	Confidence intervals or hypothesis tests about the difference of two population means. Enter your own data or summary statistics. Visualize the interval or the P-value on a graph. For two independent or two dependent samples.
Compare Two Population Proportions	Confidence intervals or hypothesis tests about the difference of two population proportions. Obtain the margin of error or the z-test statistic and visualize the interval or the P-value on a graph. For two independent or two dependent samples.
Correlation Game	Randomly generate scatterplots to guess the correlation coefficient r. Optionally, display the regression line. See how your guesses correlate with the actual values.
Describing & Exploring Categorical Data	Construct frequency and contingency tables and bar graphs to explore distributions of categorical variables. For one or two categorical variables.
Describing & Exploring Quantitative Variables	Find summary statistics and construct interactive histograms, boxplots, dotplots, or stem-and leaf plots. For one, two, or more groups.
Errors and Power in Significance Testing	Visualize and explore relationships between Type I and Type II errors and the power of a test for proportions or means. See how they depend on sample size and the true values of population parameters.
Explore Coverage of Confidence Intervals	What does “95% confidence” mean? What affects the width of an interval? Explore these concepts for confidence intervals of proportions or means, using sliders to change parameters or the sample size.
Explore Linear Regression	Create scatterplots from scratch by clicking in an empty plot to add or remove points. Investigate the effect of outliers on the correlation coefficient or regression line. Simulate linear or non-linear relationships.
Explore Time Series Data	Plot a simple time series and add a smooth or linear trend. Use preloaded data or provide your own.
Exploring MutiVariate Relationships	Construct interactive scatterplots to explore the relationship between two quantitative variables while accounting for a third (categorical or quantitative) grouping variable. Fit bivariate multiple linear regression models.
Fisher’s Exact Test	Visualize and run Fisher’s exact test for 2 x 2 contingency tables. Obtain the exact P-value for one- or two-sided tests.
Generate Random Numbers	Generate random numbers or flips of a (biased) coin. Keep track of generated numbers with a bar chart.
Inference for a Population Mean	Find confidence intervals or test hypotheses about a population mean. Enter your own data or summary statistics. Use plots to check assumptions and visualize the interval or the P-value on a graph.
Inference for a Population Proportion	Find confidence intervals or test hypotheses about a population proportion. Obtain the margin of error or the z-test statistic and visualize the interval or the P-value on a graph.
Linear Regression	Fit a simple linear regression model and obtain the regression equation and related statistics such as r-squared. Make predictions and construct confidence intervals. Display and analyze residuals.
Mean vs. Median	Explore the relationship between the mean and median for data derived from a variety of distributions or enter your own data.
Relationship Between Two Quantitative Variables: The Correlation	Construct interactive scatterplots, hover over points, move or remove points, and overlay a smooth trend line. Find the correlation coefficient r and see if it is robust to outliers. Build the sampling distribution of r via resampling.
Sampling Distribution of the Sample Mean (Continuous Population)	Experience how the sampling distribution of the sample proportion builds up one sample at a time. Use sliders to explore the shape of the sampling distribution as the sample size n increases or as the population proportion p changes. Overlay a normal distribution to explore the central limit theorem.
Sampling Distribution of the Sample Mean (Discrete Population)	Experience how the sampling distribution of the sample mean builds up one sample at a time. Use a variety of real or theoretical continuous population distributions (or create your own) from which to draw samples. Use sliders to gain a deeper understanding of the central limit theorem.
Sampling Distribution of the Sample Proportion	Experience how the sampling distribution of the sample mean builds up one sample at a time. Use a variety of real or theoretical discrete population distributions (or create your own) from which to draw samples. Use sliders to gain a deeper understanding of the central limit theorem.
The Binomial Distribution	Explore how the shape of the binomial distribution depends on the parameter n (the sample size) and p (the probability of success in a Bernoulli trial). Find and visualize probabilities of various kinds.
The Chi-Squared Distribution	See how the shape of the chi-squared distribution depends on the degrees of freedom. Find and visualize probabilities and percentiles (critical values).
The Chi-Squared Test	Test for independence, homogeneity, or goodness of fit in contingency tables. Enter your own data as raw observations or as a contingency table. Obtain observed and expected counts, and find residuals.
The F Distribution	See how the shape of the F distribution depends on the degrees of freedom. Find and visualize probabilities and percentiles (critical values).
The Normal Distribution	See how the shape of the normal distribution depends on the mean and standard deviation. Find and visualize one- and two-tailed probabilities and percentiles (critical values).
The Poisson Distribution	Explore how the shape of the Poisson distribution depends on the parameter λ (the mean). Find and visualize various kinds of probabilities.
The T Distribution	See how the shape of the t distribution depends on the degrees of freedom. Find and visualize one- and two-tailed probabilities and percentiles (critical values).

Data Sets

These data sets appear throughout the course and sometimes are easier to work with as csv or excel files. They appear in alphabetical order but the associated modules are also listed.

Data Set	Modules
Candy Rankings	X
Cats	6
Coffee Ratings	X
DC Bikeshare Winter Sample	X
Lead Moss	X
Maternal Smoke	13
Maternal Smoke Sorted	13
NHanes All Excel	5
NHanes All CSV	5
NHanes Project	5
NHanes Yes No	5
Oscars Age	3
Penguins CSV	3
Penguins Excel	3
PepsiCo	13
PGA	12
Yawn	10
School Diversity	9
Reading Level	12
	X
	X
	X
	X
	X
	X
	X

Worked Example Videos

These three amazing instructors have recorded detailed solutions for embedded practice questions in their own style and voice. This gives you the ability to learn from an instructor who explains things in a way you just “get”, or feel free to watch all three for a deeper understanding from multiple perspectives.

When you see a box that says “See Example” and “Select Instructor”, click on the dropdown menu next to “Select Instructor” and choose the instructor you’d like to watch. Then click the red box with the white arrow to play the video!

Meet the Instructors:

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