Sampling Techniques and Estimation
Sampling Techniques and Estimation tests how a sample is selected and how sample data are used to estimate population values. Expect definitions, comparisons of sampling methods, standard error, confidence intervals and sample-size calculations.
Core rules
- A parameter describes a population (μ, σ, p); a statistic describes a sample (x̄, s, p̂).
- Probability sampling includes simple random sampling, stratified sampling (divide into homogeneous strata), systematic sampling (every kth unit) and cluster sampling (select whole groups). Quota sampling is non-probability.
- Sampling error arises because a sample is used; non-sampling errors include non-response, faulty measurement and frame errors.
- Standard error of the mean is σ/√n. For large samples, a (1−α)100% confidence interval is x̄ ± z_{α/2}(σ/√n).
- Required sample size for margin of error E is n = (zσ/E)², rounded up.
Worked example
A sample of 100 items has mean 52. The population standard deviation is 10. Find a 95% confidence interval for μ. SE = 10/√100 = 1. For 95% confidence, z = 1.96. Margin of error = 1.96 × 1 = 1.96. Interval: 52 ± 1.96, that is (50.04, 53.96). Interpretation: the method gives intervals that contain μ in 95% of repeated samples.
Traps
Dividing by n instead of √n; using z when σ is unknown and n is small; saying a particular computed interval has a 95% probability of containing μ; ignoring finite population correction in small populations; and treating non-response as sampling error.