If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Unit: Module 4: Inferences and conclusions from data

0

Possible mastery points

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

Learn
Intro to theoretical probability
(Opens a modal)
Simple probability: yellow marble
(Opens a modal)
Simple probability: non-blue marble
(Opens a modal)
Intuitive sense of probabilities
(Opens a modal)
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

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

Quiz 1

Level up on the above skills and collect up to 400 Mastery points

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

Learn
Intersection and union of sets
(Opens a modal)
Compound probability of independent events
(Opens a modal)
Independent events example: test taking
(Opens a modal)
"At least one" probability with coin flipping
(Opens a modal)
Probability with Venn diagrams
(Opens a modal)
Addition rule for probability
(Opens a modal)
Addition rule for probability (basic)
(Opens a modal)
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!

Quiz 2

Level up on the above skills and collect up to 300 Mastery points

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

Learn
Shapes of distributions
(Opens a modal)
Comparing means of distributions
(Opens a modal)
Means and medians of different distributions
(Opens a modal)
Mean and standard deviation versus median and IQR
(Opens a modal)
Population standard deviation
(Opens a modal)
Sample standard deviation and bias
(Opens a modal)
The idea of spread and standard deviation
(Opens a modal)
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!

Quiz 3

Level up on the above skills and collect up to 400 Mastery points

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

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

Quiz 4

Level up on the above skills and collect up to 200 Mastery points

Topic B: Lessons 10-11: Normal distributions

Learn
Normal distribution problem: z-scores (from ck12.org)
(Opens a modal)
Comparing with z-scores
(Opens a modal)
Qualitative sense of normal distributions
(Opens a modal)
Normal distribution problems: Empirical rule
(Opens a modal)
Standard normal table for proportion below
(Opens a modal)
Standard normal table for proportion above
(Opens a modal)
Standard normal table for proportion between values
(Opens a modal)
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!

Quiz 5

Level up on the above skills and collect up to 400 Mastery points

Topic C: Lesson 12: Types of statistical studies

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

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

Learn
Identifying a sample and population
(Opens a modal)
Reasonable samples
(Opens a modal)
Techniques for generating a simple random sample
(Opens a modal)
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!

Quiz 6

Level up on the above skills and collect up to 400 Mastery points

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

Learn
Lessons 14-17: No content yet
(Opens a modal)

Topic C: Lessons 18-19: Sampling variability in the sample mean

Learn
Inferring population mean from sample mean
(Opens a modal)
Central limit theorem
(Opens a modal)
Sampling distribution of the sample mean
(Opens a modal)
Sampling distribution of the sample mean (part 2)
(Opens a modal)
Standard error of the mean
(Opens a modal)

Topic C: Lessons 20-22: Margin of error with sample means; evaluating reports with sample data

Learn
Lessons 20-22: No content yet
(Opens a modal)

Topic D: Lesson 23: Experiments and the role of random assignment

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

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

Learn
Lessons 24-27: No content yet
(Opens a modal)

Topic D: Lessons 28-29: Drawing a conclusion from an experiment

Learn
Lessons 28-29: No content yet
(Opens a modal)

Topic D: Lesson 30: Evaluating reports based on data from an experiment

Learn
Random sampling vs. random assignment (scope of inference)
(Opens a modal)
Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 2200 Mastery points!

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