Chapter 1-6: Key Vocabulary in Normal Distribution, Sampling, and Inference

Vocabulary flashcards covering core concepts from the lecture notes on normal distribution, z-scores, sampling, confidence intervals, and related errors.

Normal distribution

A symmetric, bell-shaped probability distribution that underlies many statistical methods; many inferences assume data are drawn from a normal distribution.

Z-score

A standardized score computed as (X - μ) / σ; indicates how many standard deviations a value is from the mean; mean 0, SD 1.

Raw score

The observed measurement on a variable before any transformation (e.g., height, income).

Population

The entire group of interest; has parameters such as μ (mean) and σ (standard deviation).

Sample

A subset drawn from the population used to estimate population parameters; consists of measurements on n units.

Sampling distribution of the mean

The distribution of all possible sample means from repeated samples; its mean equals μ and its standard deviation is the standard error; tends toward normal as n increases.

Standard error

The standard deviation of the sampling distribution of the mean; measures the precision of x̄ as an estimator of μ; often σ/√n.

Central Limit Theorem

As sample size grows, the sampling distribution of the mean becomes approximately normal, regardless of the population’s shape; if the population is normal, the sampling distribution is normal for any n.

Confidence interval

An interval around a sample statistic with an associated probability (e.g., 95%) that it contains the population parameter.

Sampling error

Random deviation due to using a sample rather than the full population; reduces as sample size grows.

Non-sampling error

Systematic error that persists regardless of sample size, such as measurement bias or biased sampling methods.

Selection bias

A systematic error caused by how the sample is drawn or who volunteers, leading to a non-representative sample.

Nonresponse bias

Systematic error from some subjects not responding, causing underrepresentation of certain subgroups.

Population parameter

A fixed, unknown characteristic of the population (e.g., μ, σ) that we try to estimate.

Sample statistic

A numerical summary computed from a sample (e.g., x̄, s) used to estimate population parameters.

Sample size

The number of units in a sample; influences precision and standard error.

Point estimate

A single best guess of a population parameter derived from sample data (e.g., x̄ estimates μ).

Proportion

The fraction of a binary outcome in a sample; used with CLT for proportions; normal approximation requires np > 5 and n(1-p) > 5.

Magic number 30

Rule-of-thumb that n ≥ 30 often suffices for the sampling distribution of the mean to be approximately normal.

Outlier

An observation far from the rest; can pull the mean away from the population mean.

Sign of z-score interpretation

Positive z indicates a value above the mean; negative z indicates a value below; magnitude shows distance from the mean.

Probability between a and b

For a continuous distribution, P(a < X < b) computed using z-scores; often uses the normal table.