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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
Inside Cover
Statistical Inference and Comparing Populations
At a Glance
Binder SectionProbability & Statistics
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
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.
2
Randomly select students across grades.
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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Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
Which is less biased: first 20 arrivals or 20 randomly selected names?
2
We Do
Guided Practice
A random sample can estimate a population proportion.
Two samples from the same population may give different means.
Random assignment helps balance lurking variables.
A larger difference relative to spread is stronger evidence of separation.
A confidence interval gives plausible values for a population parameter.
3
You Do
Independent Practice
Which is less biased: first 20 arrivals or 20 randomly selected names?
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
Design a sampling plan for a schoolwide question. Identify two possible biases and explain how the design reduces them.
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IXL
Compare Data Sets
Open resourceIdentify Biased Samples
Open resourceKhan Academy
Sampling Distributions
Open resourceConfidence Intervals
Open resourceDeltaMath
DeltaMath: Comparing Data Sets
Open resourceDeltaMath: Sampling and Statistical Inference
Open resource
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Before you begin, I can…
- 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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Question 1
What should happen before calculating?
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Question 2
Which response gives the strongest evidence?
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Question 3
What is an effective accuracy check?
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Question 4
Why are units or labels important?
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Question 5
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