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Statistical Inference and Comparing Populations

Students use samples to estimate population characteristics and compare distributions with measures of center and variability.

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Beginner 15–20 minutes Probability & Statistics
Probability & Statistics Page 7 of 8
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At a Glance

Statistical Inference and Comparing Populations
Binder SectionProbability & Statistics
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
Essential Question

When does a sample support a trustworthy conclusion about a population?

Build Understanding

Statistical inference uses sample evidence to make a reasoned statement about a population. Random sampling supports generalization; random assignment supports cause-and-effect conclusions.

Compare populations using the same displays and appropriate measures of center and spread. Consider whether a difference is large relative to the variability and recognize that sample results naturally vary.

Visual Model
4Thousands 3Hundreds 2Tens 7Ones

4,327 = 4,000 + 300 + 20 + 7

Goals

Learning Targets

  • Samples estimate population characteristics.
  • Random sampling supports generalization.
  • Random assignment supports causal conclusions.
  • Compare both center and spread.
  • Sampling variability is expected.
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Interactive Vocabulary

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Worked Examples

Example 1

Survey school lunch preference

1

Sampling only cafeteria workers is biased.

Example 2

18 of 30 sampled students prefer option A

1

Estimate 60% of a similar population, with uncertainty.

Ask and explain

Common Questions

Does one sample give the exact population value? No.
Can an observational study prove causation? Usually no.
Why compare spread as well as center? A difference in centers may be small relative to natural variation.
Notice and correct

Common Misconceptions

Using a convenience sample

Identify who is excluded.

Treating an estimate as exact

Report it as an inference and discuss uncertainty.

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Populations and Samples lesson and examples

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Quick Start

Warm-Up

Warm-up 1

Directions: Solve the problem. Show your thinking, then enter only your final answer.

Which is less biased: first 20 arrivals or 20 randomly selected names?

Picture the dataUse the picture to organize what you know before you solve.
look for center, spread, and patterns

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2
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Guided Practice

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You Do

Independent Practice

Independent 1

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Which is less biased: first 20 arrivals or 20 randomly selected names?

Picture the dataUse the picture to organize what you know before you solve.
look for center, spread, and patterns

Choose how you want to work or answer.

Independent 2

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Create and solve a second example with different values.

Picture the dataUse the picture to organize what you know before you solve.
look for center, spread, and patterns

Choose how you want to work or answer.

4
Stretch Your Thinking

Challenge & Real-World Practice

🧩 Challenge

Design a sampling plan for a schoolwide question. Identify two possible biases and explain how the design reduces them.

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  • I can identify the important information.
  • I can use accurate notation, labels, and units.
  • I can justify and verify my conclusion.
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What should happen before calculating?

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Question 2

Which response gives the strongest evidence?

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What is an effective accuracy check?

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Why are units or labels important?

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