Samples and estimation
Estimate population features from samples and explain confidence intervals and their conditions.
Meaning
Estimation uses a sample to learn about unknown population features. Margins of error and confidence intervals account for how estimates vary across samples. Changing the sample changes the central estimate, so a single number does not show its uncertainty. Interval width uses the variability of the sample mean and an assumed distribution. At the same confidence level, greater variability generally requires a wider interval.
Example
If many samples are drawn by the same method and a 95% confidence interval is constructed each time, the procedure is designed so that about 95% of those intervals contain the fixed population mean. Do not immediately interpret a particular calculated interval as having a 95% probability of containing the fixed mean. The confidence level describes the repeated interval-construction procedure.
Practice for this concept
Scope and references
Topics
Sampling, sample means, sampling distributions, estimation, confidence intervals
Learning goal
Estimate population features from samples and explain confidence intervals and their conditions.
Helpful background
Review populations, samples, and the probability assumptions of the estimation method.
Sampling and estimation
These choice exercises calculate or judge specified finite data, trials, or assumptions. They do not establish data collection, written inference, model validation, or mastery of the whole statistics area.