Understand sampling methods, bias, and how to make valid inferences from sample data to populations.
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?
A
65% of all Americans support the park
B
About 65% of adults in City X likely support the park
C
Exactly 65% of adults in City X support the park
D
The park should be built
B
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?
A
Selection bias
B
Voluntary response bias
C
Response bias
D
No bias — this is a census
B
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.
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.
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.
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