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Sample Survey — Definition, Formula & Examples

A sample survey is a study that asks questions of, or measures, a selected group of people or items so you can draw conclusions about a much larger group without checking every member.

A sample survey is an observational study in which data are collected from a subset of units (the sample), chosen from a defined population by a stated sampling design, in order to estimate population parameters. No treatment is imposed. This separates it from an experiment, and studying only a subset separates it from a census.

Key Formula

p^=xn\hat{p} = \frac{x}{n}
Where:
  • p^\hat{p} = sample proportion, the survey's estimate of the population proportion pp
  • xx = number of sampled units with the characteristic of interest
  • nn = sample size (number of units surveyed)

Worked Example

Problem: A school has 2,000 students. The student council surveys a simple random sample of 200 students, and 120 of them say they favor a later start time. Estimate the proportion and the number of all students who favor a later start.
Step 1: Identify the population, the sample, and the sampling fraction. The population is all 2,000 students. The sample is the 200 students who were surveyed.
2002000=0.10=10%\frac{200}{2000} = 0.10 = 10\%
Step 2: Compute the sample proportion. Random selection makes it a reasonable estimate of the population proportion.
p^=120200=0.60\hat{p} = \frac{120}{200} = 0.60
Step 3: Scale the proportion up to the whole population.
0.60×2000=12000.60 \times 2000 = 1200
Answer: An estimated 60% of students, or about 1,200 of the 2,000, favor a later start. This is an estimate, so a different random sample would likely give a slightly different value.

Why It Matters

In AP Statistics, you must classify a study as a sample survey, an experiment, or a census before you decide what conclusions it supports. A survey can estimate how common something is. It cannot show cause and effect. Election polls, market research, and the U.S. Census Bureau's American Community Survey all rely on sample survey design.

Common Mistakes

Mistake: Believing that a very large sample guarantees accurate results.
Correction: A large sample reduces random variation, but it does not fix bias. In 1936, the Literary Digest received about 2.4 million responses and predicted that Landon would win. Roosevelt won in a landslide, because the magazine drew its mailing list largely from car and telephone owners and only some people mailed back responses. Judge a survey first by how the sample was selected, then by its size.

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