Essentials of Statistics for Business & Economics - Chapter 7: Sampling and Sampling Distributions

Vocabulary practice flashcards covering key statistical concepts, sampling techniques, estimators, sampling distributions, and errors from Chapter 7 of Essentials of Statistics for Business & Economics.

Element

The entity on which data are collected.

Population

A collection of all the elements of interest.

Sample

A subset of the population.

Frame

A list of the elements that the sample will be selected from.

Sampled Population

The population from which the sample is actually drawn.

Target Population

The population about which researchers want to make statistical inferences.

Parameter

A numerical characteristic of a population, such as the population mean ($\mu$), population standard deviation ($\sigma$), or population proportion ($p$).

Simple Random Sample (Finite Population)

A sample of size $n$ selected from a finite population of size $N$ in such a way that each possible sample of size $n$ has the same probability of being selected.

Sampling with Replacement

A sampling procedure where each sampled element is returned to the population before subsequent elements are selected, allowing an element to appear in the sample more than once.

Sampling without Replacement

A sampling procedure where each sampled element is not returned to the population before selecting subsequent elements, ensuring each element appears in the sample at most once.

Random Sample (Infinite Population)

A sample of size $n$ selected from an ongoing process or infinite population such that each element selected comes from the same population and each element is selected independently.

Point Estimator

A sample statistic (such as $\bar{x}$, $s$, or $\bar{p}$) used to estimate the value of an unknown population parameter.

Point Estimate

The numerical value of a sample statistic obtained from a specific sample and used as an estimate of a population parameter.

Sampling Distribution

A probability distribution consisting of all possible values of a sample statistic.

Standard Error

The standard deviation of a point estimator, which measures the dispersion of the estimator's sampling distribution.

Finite Population Correction Factor

The factor $\sqrt{\frac{N - n}{N - 1}}$, used to adjust the standard error of a point estimator when sampling without replacement from a finite population of size $N$; it can be neglected when $\frac{n}{N} < 0.05$.

Central Limit Theorem

A theorem stating that in selecting random samples of size $n$ from a population, the sampling distribution of the sample mean $\bar{x}$ can be approximated by a normal distribution as the sample size becomes large (typically when $n \ge 30$).

Unbiased Estimator

A property of a point estimator $\hat{\theta}$ where the expected value of the sample statistic equals the population parameter being estimated, meaning $E(\hat{\theta}) = \theta$.

Relative Efficiency

A property comparing two unbiased point estimators, where the estimator with the smaller standard error or variance is preferred as having greater relative efficiency.

Consistency

A property of a point estimator where its values tend to get closer to the population parameter as the sample size becomes larger.

Stratified Random Sampling

A probability sampling method in which the population is first divided into homogeneous groups called strata, and a simple random sample is independently selected from each stratum.

Cluster Sampling

A probability sampling method in which the population is divided into separate heterogeneous groups called clusters (each ideally a small-scale version of the population), a simple random sample of clusters is selected, and all elements within the chosen clusters form the sample.

Systematic Sampling

A probability sampling method in which one element is randomly selected from the first $N/n$ elements on a population list, followed by selecting every $N/n\text{-th}$ element thereafter.

Convenience Sampling

A nonprobability sampling technique in which sample elements are selected primarily on the basis of ease of access without known probabilities of selection.

Judgment Sampling

A nonprobability sampling technique in which an expert or knowledgeable individual selects sample elements that they judge to be most representative of the population.

Sampling Error

The natural deviation of a sample statistic from the population parameter that results from random sampling.

Nonsampling Error

Deviations of the sample from the population that occur for reasons other than random sampling, including coverage, nonresponse, measurement, interviewer, and processing errors.

Coverage Error

A nonsampling error that occurs when the research objective and the frame or sampled population are not aligned, typically caused by omitted or duplicated elements.

Nonresponse Error

A nonsampling error that occurs in surveys when particular segments of the population are systematically more or less likely to respond to the survey mechanism.

Big Data

Any set of data that is too large or too complex to be handled by standard data-processing techniques and typical desktop software, characterized by volume, variety, veracity, and velocity.

Tall Data

A data set dimension characterized by having so many observations that traditional statistical inference is rendered obsolete.

Wide Data

A data set dimension characterized by having so many variables that their simultaneous consideration is rendered infeasible.