Central Limit Theorem and Sampling Distributions

These flashcards focus on key vocabulary and definitions related to the Central Limit Theorem and sampling distributions in statistics.

Central Limit Theorem

The theorem stating that as the sample size (n) increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Sampling Distribution

The distribution of sample means over repeated sampling from a population.

Mean of Sampling Distribution (μx)

The mean of the sampling distribution of the sample mean equals the population mean (μ).

Variance of Sampling Distribution

For finite populations, the variance of the sample mean is σ²/n(1 - n/N), where σ² is the population variance.

Standard Deviation of Sampling Distribution (σx)

The standard deviation of the sampling distribution of the sample means is σ/√n.

Population Mean (μ)

The average of a group from which samples are drawn.

Sample Size (n)

The number of observations in a sample drawn from a population.

Z-score Formula

The formula used to find the standardized value: z = (X - μ) / σ.

Probability (P)

The likelihood of an event occurring, expressed as a number between 0 and 1.

Z-table

A table that provides the area (probability) to the left of a given z-score in a standard normal distribution.