SCM EXAM 2 WEEK 7 (Sampling and Sampling Distributions)

Key vocabulary terms and definitions covering sampling techniques, bias types, estimators, sampling distributions, and the Central Limit Theorem from Chapter 7.

Major portion of statistics is concerned with

STATISTICAL INFERENCE

Population

All items of interest in a statistical problem.

Simple Random Sample

A sample of $n$ observations that has the same probability of being selected as any other sample of $n$ observations.

• most statistical methods assume a simple random variable

Stratified Random Sample and advantaged of it

A sampling method where the population is divided into mutually exclusive and collectively exhaustive groups called strata, and simple random samples are drawn from each stratum proportionally to its size in the population.

• pop. subgroups of interest are ENSURED to be represented in the sample.

• estimates of parameters have greater precision than estimates obtained from simple random sampling.

Cluster Sampling

A sampling method where the population is divided into mutually exclusive and collectively exhaustive groups called clusters, and all observations from randomly selected clusters are included in the sample.

ADVANTAGES: CHEAPER

DISADVANTAGES: LESS PRECISION

Selection Bias

A systematic underrepresentation of certain groups from consideration for the sample.

Nonresponse Bias

A systematic difference in answers between respondents and nonrespondents to a survey.

Social-Desirability Bias

A systematic difference between a group's "socially acceptable" responses and their actual preferences.

Population Parameter

• A numerical summary of a population,

• such as the population mean summarizing a quantitative variable

• or the population proportion summarizing a categorical variable.

TRUE OF FALSE: the value of a population parameter is often unknown

TRUE

Point Estimator

A sample statistic used to estimate the value of an unknown population parameter.

Unbiased Estimator

An estimator whose expected value equals the true population parameter being estimated.

Estimate

A particular numerical value taken by an estimator for a specific sample.

Sampling Distribution of the Sample Mean

The probability distribution derived from all possible samples of a given size, $n$, from the population.

What is the standard deviation of X also referred to

STANDARD ERROR

Standard Error of the Sample Mean

The standard deviation of the sampling distribution of the sample mean, calculated as $\text{se}(\bar{X}) = \frac{\sigma}{\sqrt{n}}$.

Central Limit Theorem (CLT) for the Sample Mean

A theorem stating that for any population with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of $\bar{X}$ is approximately normal if the sample size is sufficiently large, generally justified when $n \ge 30$.

Sample Proportion

The statistic $P = \frac{X}{n}$, defined as the number of successes $X$ divided by the sample size $n$, which serves as an unbiased estimator of the population proportion $p$.

Standard Error of the Sample Proportion

The standard deviation of the sampling distribution of the sample proportion, calculated as $\text{se}(P) = \sqrt{\frac{p(1 - p)}{n}}$.

Normal Approximation Condition for Sample Proportion

The general guideline under the Central Limit Theorem stating that the sampling distribution of $P$ is approximately normally distributed when $n p \ge 5$ and $n(1 - p) \ge 5$.