Sampling, margin of error and study design · SAT · Courselo

Lesson 6 of 6 · Problem-solving and data analysis

Sampling, margin of error and study design

7 min read · about 1 h with practice3 quick checks<1% of the testCore

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These questions test whether you know what a survey or study can prove and what it can’t. Most are multiple-choice “which conclusion is most appropriate?” items with little or no arithmetic. The right answer claims exactly what the design supports, no more and no less. A few are quick calculations that scale a sample result up to a population. Expect about one per test in Problem-Solving and Data Analysis, and treat it as a point you should never lose.

By the end you’ll be able to

Use a sample statistic to estimate a population value, and interpret a margin of error as a range of plausible values
Explain how sample size and variability affect the margin of error
Decide what a study supports: random sampling allows generalizing to the population; random assignment allows cause-and-effect conclusions
Identify sampling bias and conclusions that go beyond the study design

What the exam asks

Question type	What decides it
Estimate a population count from a sample	sample proportion × population size
Interpret a margin of error	estimate ± margin of error gives plausible values for the population value
Effect of sample size or variability	a larger sample gives a smaller margin; more spread in the data gives a larger one
Largest group the results apply to	the population that was randomly sampled
Cause and effect or only association?	whether treatments were randomly assigned
Spot the bias	how the sample was chosen

Core ideas

From sample to population

A random sample’s proportion estimates the population proportion.

\text{estimated count} = \frac{\text{sample count}}{\text{sample size}} \times \text{population size}

Check your understanding

3 questions on sampling, margin of error and study design. Every option is explained once you answer.

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Flashcards

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PromptCard 1 of 3

What does a margin of error tell you?

Change (same population and method)	Margin of error
Larger random sample	smaller
Smaller random sample	larger
More variable data (larger standard deviation)	larger
Higher confidence level (99% vs. 95%)	larger

	Random assignment	No random assignment
Random selection	Cause and effect, for the whole sampled population	Association, for the whole sampled population
No random selection	Cause and effect, for subjects like these only	Association, for the sample only

Sampling, margin of error and study design

By the end you’ll be able to

What the exam asks

Core ideas

From sample to population

Check your understanding

Flashcards

Margin of error

What changes the margin of error

The two design questions

Bias

Comparing two estimates

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

Core ideas

From sample to population

vii.Check your understanding

viii.Flashcards

Margin of error

What changes the margin of error

The two design questions

Bias

Comparing two estimates

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards