Problem Solving & Data Analysis Hard
⏱ 15 min 📊 Hard ⭐ Premium

Inference from Sample Statistics

Understand sampling methods, bias, and how to make valid inferences from sample data to populations.

Before you read
Answer first — see what you already know.

A city planner surveys 200 randomly selected residents of City X and finds that 65% support building a new public park. Which conclusion is best supported?

Check your answer
Answer:

B

Before you read
Answer first — see what you already know.

A restaurant asks diners to rate their meal online. The average rating is 1.8 out of 5 stars. What type of bias most likely affects this result?

Check your answer
Answer:

B

Theory

Sampling and Populations

Population: The entire group you want to study.
Sample: A subset of the population that you actually measure.

A good sample is representative — it reflects the characteristics of the population.

Random sample: Every member of the population has an equal chance of being selected. This is the gold standard for avoiding bias.

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Sample mean ± margin of error
Theory

Types of Bias

Selection bias: The sample systematically excludes certain groups. Example: surveying only gym members about exercise habits.

Response bias: People don't answer truthfully. Example: asking about illegal activities face-to-face.

Nonresponse bias: Certain types of people don't respond. Example: busy people skip long surveys.

Voluntary response bias: Only people with strong opinions respond. Example: online reviews tend to be extreme.

Example 1

A school wants to know if students support a longer lunch. They survey students in the cafeteria during lunch. Is this a good sample?

This has selection bias — students in the cafeteria during lunch are more likely to care about lunch policies.

Students who don't eat in the cafeteria are excluded.

A random sample from the entire student body would be better.

No — this sample has selection bias.

Continue this lesson in the app

2 more sections including examples, practice problems, and step-by-step solutions.

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