Samples, Surveys, and Statistical Claims

A reliable method

1. Identify the population and sample.
2. Check how participants were selected and whether important groups were missed.
3. Distinguish an observational study from a randomized experiment.
4. Report uncertainty and avoid claims stronger than the study design supports.

Example 1

A random sample of 200 town residents includes 84 who favor a proposal. Find the sample proportion.

1. The numerator counts sampled supporters, not all residents.
2. Divide 84 by the sample size 200.
3. 84/200=0.42, or 42%. This is a sample estimate, not an exact population percentage.

Answer: \(21/50\) or 42%

Example 2

A survey reports 54% with a margin of error of 4 percentage points. Give its stated interval.

1. Subtract 4 percentage points from 54%.
2. Add 4 percentage points to 54%.
3. The stated interval is 50% to 58%; the reported confidence level, if supplied, governs its statistical interpretation.

Answer: \([50,58]\) percent

Common mistakes

• A large convenience sample can still be biased.
• Association in an observational study is not, by itself, evidence of causation.

Practice without the answer first

1. In a sample of 150 people, 36 use a bus. Estimate how many of 2,000 residents use a bus if that sample is representative.
2. A sample mean is 72 with a reported margin of error 3. Give the interval on the same measurement scale.
3. A sample has 45 successes in 180 trials. Estimate the success percentage.

These original skill exercises are not official exam questions or a score prediction. Use the coverage notes on your exam hub to choose relevant practice.