Sampling

A simple random sample is a subset of a larger population created in such a way that each element of the population has an equal probability of being selected to the subset.

With systematic sampling, we select every k^th member until we have a sample of the desired size. The sample that results from this procedure should be approximately random.

Sampling error is the difference between the observed value of a statistic and the quantity it is intended to estimate.

A sample statistic is a random variable.

In stratified random sampling, the population is divided into subpopulations (strata) based on one or more classification criteria. Simple random samples are then drawn from each stratum in sizes proportional to the relative size of each stratum in the population. These samples are then pooled to form a stratified random sample.

A time series is a sequence of returns collected at discrete and equally spaced intervals of time.

Cross-sectional data are data on some characteristic of individuals, groups, geographical regions, or companies at a single point in time.

[Practice Problems] The best approach for creating a stratified random sample of a population involves:

A drawing an equal number of simple random samples from each subpopulation.

B selecting every k^th member of the population until the desired sample size is reached.

C drawing simple random samples from each subpopulation in sizes proportional to the relative size of each subpopulation.

[Solutions] C

Stratified random sampling involves dividing a population into subpopulations based on one or more classification criteria. Then, simple random samples are drawn from each subpopulation in sizes proportional to the relative size of each subpopulation. These samples are then pooled to form a stratified random sample.