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Module 4: Inferences and conclusions from data

Topic A: Lesson 1: Chance experiments, sample spaces, and events

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Intro to theoretical probability
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Simple probability: yellow marble
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Simple probability: non-blue marble
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Intuitive sense of probabilities
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Practice
Simple probabilityGet 5 of 7 questions to level up!
Comparing probabilitiesGet 5 of 7 questions to level up!

Topic A: Lessons 2-4: Two-way tables, conditional probability, and independence

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Calculating conditional probability
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Conditional probability explained visually
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Conditional probability using two-way tables
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Conditional probability and independence
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Conditional probability and independence
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Analyzing event probability for independence
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Practice
Calculating conditional probabilityGet 3 of 4 questions to level up!
Dependent and independent eventsGet 3 of 4 questions to level up!

Topic A: Lessons 5-7: Venn diagrams and probability rules

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Intersection and union of sets
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Compound probability of independent events
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Independent events example: test taking
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Coin flipping probability
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Probability with Venn diagrams
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Addition rule for probability
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Addition rule for probability (basic)
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Practice
Independent probabilityGet 3 of 4 questions to level up!
Probabilities of compound eventsGet 3 of 4 questions to level up!
Two-way tables, Venn diagrams, and probabilityGet 3 of 4 questions to level up!

Topic B: Lesson 8: Distributions—Center, shape, and spread

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Shapes of distributions
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Comparing means of distributions
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Means and medians of different distributions
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Mean and standard deviation versus median and IQR
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Population standard deviation
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Sample standard deviation and bias
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The idea of spread and standard deviation
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Practice
Shape of distributionsGet 3 of 4 questions to level up!
Calculating the meanGet 3 of 4 questions to level up!
Calculating the mean: data displaysGet 3 of 4 questions to level up!
Sample and population standard deviationGet 3 of 4 questions to level up!

Topic B: Lesson 9: Using a curve to model a data distribution

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Density Curves
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Median, mean and skew from density curves
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Density curve worked example
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Worked example finding area under density curves
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Practice
Properties of density curvesGet 3 of 4 questions to level up!
Area under density curvesGet 3 of 4 questions to level up!

Topic B: Lessons 10-11: Normal distributions

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Normal distribution problem: z-scores (from ck12.org)
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Comparing with z-scores
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Qualitative sense of normal distributions (from ck12.org)
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Normal distribution problems: Empirical rule (from ck12.org)
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Standard normal table for proportion below
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Standard normal table for proportion above
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Standard normal table for proportion between values
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Practice
Calculating z-scoresGet 3 of 4 questions to level up!
Empirical ruleGet 3 of 4 questions to level up!
Normal distribution: Area above or below a pointGet 3 of 4 questions to level up!
Normal distribution: Area between two pointsGet 3 of 4 questions to level up!

Topic C: Lesson 12: Types of statistical studies

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Types of statistical studies
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Worked example identifying experiment
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Worked example identifying observational study
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Worked example identifying sample study
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Observational studies and experiments
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Correlation and causality
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Practice
Types of statistical studiesGet 3 of 4 questions to level up!

Topic C: Lesson 13: Using sample data to estimate a population characteristic

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Identifying a sample and population
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Reasonable samples
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Techniques for generating a simple random sample
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Practice
Identifying the population and sampleGet 3 of 4 questions to level up!
Valid claimsGet 3 of 4 questions to level up!
Simple random samplesGet 3 of 4 questions to level up!

Topic C: Lessons 14-17: Sample proportions, sampling variability, margin of error

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Lessons 14-17: No content yet
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Topic C: Lessons 18-19: Sampling variability in the sample mean

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Inferring population mean from sample mean
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Central limit theorem
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Sampling distribution of the sample mean
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Sampling distribution of the sample mean 2
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Standard error of the mean
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Topic C: Lessons 20-22: Margin of error with sample means; evaluating reports with sample data

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Lessons 20-22: No content yet
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Topic D: Lesson 23: Experiments and the role of random assignment

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Types of statistical studies
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Worked example identifying experiment
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Worked example identifying observational study
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Observational studies and experiments
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Introduction to experiment design
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Matched pairs experiment design
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The language of experiments
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Principles of experiment design
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Random sampling vs. random assignment (scope of inference)
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Practice
Types of statistical studiesGet 3 of 4 questions to level up!

Topic D: Lessons 24-27: Ruling out differences due to random assignment

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Lessons 24-27: No content yet
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Topic D: Lessons 28-29: Drawing a conclusion from an experiment

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Lessons 28-29: No content yet
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Topic D: Lesson 30: Evaluating reports based on data from an experiment

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Random sampling vs. random assignment (scope of inference)
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About this unit

"Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability. The idea of using a smooth curve to model a data distribution is introduced along with using tables and technology to find areas under a normal curve. Students make inferences and justify conclusions from sample surveys, experiments, and observational studies. Data is used from random samples to estimate a population mean or proportion. Students calculate margin of error and interpret it in context. Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments." Eureka Math/EngageNY (c) 2015 GreatMinds.org